\relax \bibstyle{abbrvnat} \pagetypeorder{rRn} \ifx\hyper@anchor\@undefined \global \let \oldcontentsline\contentsline \gdef \contentsline#1#2#3#4{\oldcontentsline{#1}{#2}{#3}} \global \let \oldnewlabel\newlabel \gdef \newlabel#1#2{\newlabelxx{#1}#2} \gdef \newlabelxx#1#2#3#4#5#6{\oldnewlabel{#1}{{#2}{#3}}} \AtEndDocument{\let \contentsline\oldcontentsline \let \newlabel\oldnewlabel} \else \global \let \hyper@last\relax \fi \@writefile{lof}{\vskip 0.55in {\bfseries Figure}\hfill {\bfseries Page}\vskip 0.25em\rm } \@writefile{lot}{\vskip 0.55in {\bfseries Table}\hfill {\bfseries Page} \vskip 0.25em\rm } \@writefile{toc}{\nobreakspace {}\hfill {{\bfseries Page}}} \aioptions{0|{vv }{ll}{, ff}{, jj}|9999|9999|pages} \aifilename{optimal_foraging_theory.ain} \@writefile{toc}{\contentsline {front}{{Abstract}}{iii}{chapter*.1}} \@writefile{toc}{\contentsline {front}{{Dedication}}{iv}{section*.2}} \aiexplicit{Kenneth Timmons}{\hyperpage{iv}} \@input{oft_ch0_ack.aux} \@input{oft_ch0_vita.aux} \@writefile{toc}{\contentsline {front}{{List of Tables}}{xi}{chapter*.6}} \@writefile{toc}{\contentsline {front}{List of Figures}{xii}{chapter*.7}} \@input{oft_ch1_intro.aux} \@input{oft_ch2_model.aux} \@input{oft_ch3_optimization_objectives.aux} \@input{oft_ch4_optimization_results.aux} \@input{oft_ch5_conclusion.aux} \@input{oft_zapp_markov_encounter_sto_limits.aux} \bibdata{optimal_foraging_theory} \aibibcite{APW04}{1} \bibcite{APW04}{{1}{2004}{{Andrews et~al.}}{{Andrews, Passino, and Waite}}} \aibibcite{APW06}{2} \bibcite{APW06}{{2}{2007}{{Andrews et~al.}}{{Andrews, Passino, and Waite}}} \aibibcite{HA99}{3} \bibcite{HA99}{{3}{1999}{{Arkes and Ayton}}{{}}} \aibibcite{BK95}{4} \bibcite{BK95}{{4}{1995}{{Bateson and Kacelnik}}{{}}} \aibibcite{BW96}{5} \bibcite{BW96}{{5}{1996}{{Bateson and Whitehead}}{{}}} \aibibcite{Bawa75}{6} \bibcite{Bawa75}{{6}{1975}{{Bawa}}{{}}} \aibibcite{Bawa78}{7} \bibcite{Bawa78}{{7}{1978}{{Bawa}}{{}}} \aibibcite{Bawa82}{8} \bibcite{Bawa82}{{8}{1982}{{Bawa}}{{}}} \aibibcite{BL77}{9} \bibcite{BL77}{{9}{1977}{{Bawa and Lindenberg}}{{}}} \aibibcite{Bertsekas95}{10} \bibcite{Bertsekas95}{{10}{1995}{{Bertsekas}}{{}}} \aibibcite{Caraco80}{11} \bibcite{Caraco80}{{11}{1980}{{Caraco}}{{}}} \aibibcite{CB05}{12} \bibcite{CB05}{{12}{2005}{{Carmel and Ben-Haim}}{{}}} \@writefile{symbols}{\indexentry{*conventions@[{[\texttt {xx}]}] see reference number \texttt {xx} in \hyperref [ch:bibliography]{the bibliography}|nopage}{100}} \@writefile{symbols}{\indexentry{Ageneral.0@[$=$] \index {mathematics"!equality ($=$)"|indexglo}is equal to|nopage}{100}} \@writefile{symbols}{\indexentry{Ageneral.0@[$\triangleq $] \index {mathematics"!definition ($\triangleq $)"|indexglo}defined as|nopage}{100}} \@writefile{symbols}{\indexentry{Csets.0@[$\set {X}$] a set $\set {X}$|nopage}{100}} \@writefile{symbols}{\indexentry{Csets.1a@[$\{a,b,c\}$] a set of objects $a$, $b$, and $c$|nopage}{100}} \@writefile{symbols}{\indexentry{Csets.1aa@[$\dots $] continue the established pattern \adinfinitum {} (\eg {}, the infinite set $\{1,2,3,\dots \}$)|nopage}{100}} \@writefile{symbols}{\indexentry{Csets.1b@[$\emptyset $] \index {mathematics"!sets"!empty set ($\emptyset $)"|indexglo}the empty set (\ie {}, $\{\}$)|nopage}{100}} \@writefile{symbols}{\indexentry{Csets.1b@[$\in $] is an element of (\ie {}, \index {mathematics"!sets"!set element ($\in $)"|indexglo}set inclusion)|nopage}{100}} \@writefile{symbols}{\indexentry{Csets.1b@[$\notin $] is not an element of (\ie {}, \index {mathematics"!sets"!exclusion ($\notin $)"|indexglo}set exclusion)|nopage}{100}} \@writefile{symbols}{\indexentry{Csets.1c@[$\subseteq $ ($\supseteq $)] is a \index {mathematics"!sets"!subset ($\subseteq $ or $\subset $)"|indexglo}subset (superset) of|nopage}{100}} \@writefile{symbols}{\indexentry{Csets.1d@[$\set {X} = \set {Y}$] set $\set {X}$ is equal to set $\set {Y}$ (\ie {}, $\set {X} \subseteq \set {Y}$ and $\set {Y} \subseteq \set {X}$)|nopage}{100}} \@writefile{symbols}{\indexentry{Csets.1d@[$\set {X} \neq \set {Y}$] set $\set {X}$ is not equal to set $\set {Y}$|nopage}{100}} \@writefile{symbols}{\indexentry{Csets.1c@[$\subset $ ($\supset $)] is a \index {mathematics"!sets"!superset ($\supseteq $ or $\supset $)"|indexglo}proper/strict subset (superset) of|nopage}{100}} \@writefile{symbols}{\indexentry{Csets.1ab@[$\{ u : p \}$] set of all elements of $u$ such that $p$|nopage}{100}} \@writefile{symbols}{\indexentry{Csets.1ab@[$\{ u : p, q, r \}$] set of all elements of $u$ such that $p$, $q$, and $r$|nopage}{100}} \@writefile{symbols}{\indexentry{Dseq.0@[$x(i)$~or~$x_i$~or~$x^i$] alternate notations for an index $i$ on a symbol $x$|nopage}{100}} \@writefile{symbols}{\indexentry{Csets.2cart0@[$(a,b)$] \index {mathematics"!ordered pair"|indexglo}ordered pair of objects $a$ and $b$ (\ie {}, $(a,b) \triangleq \{\{a\},\{a,b\}\}$)|nopage}{100}} \@writefile{symbols}{\indexentry{Csets.2cart01@[$(x_1,x_2,\dots ,x_n)$] $n$-tuple (\ie {}, \index {mathematics"!n-tuple"@$n$-tuple"|indexglo}tuple of length $n \in \N $ with coordinates $x_1$, $x_2$,\dots ,$x_n$ in their respective order)|nopage}{100}} \@writefile{symbols}{\indexentry{Csets.2cart1@[$\set {X} \times \set {Y}$] \index {mathematics"!sets"!Cartesian product ($\times $)"|(indexglo}(binary) \aimention {Ren\'{e} Descartes}Cartesian product of sets $\set {X}$ and $\set {Y}$ (\ie {}, $\set {X} \times \set {Y} \triangleq \{(x,y):x \in \set {X}, y \in \set {Y}\}$)|nopage}{100}} \@writefile{symbols}{\indexentry{Csets.2cart10@[$\set {X}_1 \times \cdots \times \set {X}_n$] \aimention {Ren\'{e} Descartes}Cartesian product of $n$ sets $\set {X}_1$, \dots , $\set {X}_n$ (\ie {}, $\set {X}_1 \times \cdots \times \set {X}_n \triangleq \{(x_1,\dots ,x_n):x_1 \in \set {X}_1, \dots , x_n \in \set {X}_n\}$)|nopage}{100}} \@writefile{symbols}{\indexentry{Csets.2cart11@[$\set {X}^n$] \aimention {Ren\'{e} Descartes}Cartesian product of set $\set {X}$ with itself $n$ times (\eg {}, $\set {X}^3 \triangleq \set {X} \times \set {X} \times \set {X}$)\index {mathematics"!sets"!Cartesian product ($\times $)"|)indexglo}|nopage}{100}} \@writefile{symbols}{\indexentry{Ganalysis.0011@[$f: \set {X} \mapsto \set {Y}$] a \index {mathematics"!functions"|indexglo}function $f$ with domain $\set {X}$ and codomain $\set {Y}$|nopage}{100}} \@writefile{symbols}{\indexentry{Dseq.1@[$(x_i:i \in \set {I})$] an indexed family with index set $\set {I}$ (also $(x_i)_{i \in \set {I}}$)|nopage}{100}} \@writefile{symbols}{\indexentry{Dseq.2@[$(x(t):t \geq 0)$] an ordered indexed family with a directed index set $\set {T}$ where $0 \in \set {T}$|nopage}{100}} \@writefile{symbols}{\indexentry{Csets.1zz@[$\pipe \set {X}\pipe $] cardinality of set $\set {X}$|nopage}{100}} \@writefile{symbols}{\indexentry{Csets.1z@[$\Pow (\set {U})$] \index {mathematics"!sets"!power set ($\Pow $)"|indexglo}power set of set $\set {U}$ (\ie {}, the set of all subsets of $\set {U}$)|nopage}{100}} \@writefile{symbols}{\indexentry{Csets.207@[$\set {X}^c$] \index {mathematics"!sets"!set complement (${}^c$)"|indexglo}complement of set $\set {X}^c$ (\eg {}, $\set {U} \setdiff \set {X}$ where $\set {X} \subseteq \set {U}$)|nopage}{100}} \@writefile{symbols}{\indexentry{Csets.202@[$\set {X} \cup \set {Y}$] \index {mathematics"!sets"!set union ($\cup $)"|indexglo}set union (or join) of sets $\set {X}$ and $\set {Y}$|nopage}{100}} \@writefile{symbols}{\indexentry{Csets.2@[$\bigcup $] union of many sets (compare to $\sum $)|nopage}{100}} \@writefile{symbols}{\indexentry{Csets.201@[$\set {X} \cap \set {Y}$] \index {mathematics"!sets"!set intersection ($\cap $)"|indexglo}set intersection (or meet) of sets $\set {X}$ and $\set {Y}$|nopage}{100}} \@writefile{symbols}{\indexentry{Csets.2@[$\bigcap $] intersection of many sets (compare to $\sum $)|nopage}{100}} \@writefile{symbols}{\indexentry{Csets.203@[$\set {X} \setdiff \set {Y}$] \index {mathematics"!sets"!set difference ($\setdiff $)"|indexglo}difference of sets $\set {X}$ and $\set {Y}$|nopage}{100}} \@writefile{symbols}{\indexentry{Elogic@[$\implies $] \index {mathematics"!logic"!implication ($\implies $)"|indexglo}logical implication|nopage}{100}} \@writefile{symbols}{\indexentry{Elogic@[$\iff $] \index {mathematics"!logic"!equivalence ($\iff $)"|indexglo}logical equivalence|nopage}{100}} \@writefile{symbols}{\indexentry{Ageneral.5@[$\leq $ ($\geq $)] less (greater) than or equal to|nopage}{100}} \@writefile{symbols}{\indexentry{Ageneral.5@[$<$ ($>$)] strictly less (greater) than|nopage}{100}} \@writefile{symbols}{\indexentry{Csets.2intervals1@[${[a,b]}$] \index {mathematics"!numbers"!real number intervals"|(indexglo}interval $[a,b] \triangleq \{ x \in \set {X} : a \leq x \leq b \}$|nopage}{100}} \@writefile{symbols}{\indexentry{Csets.2intervals2@[${(a,b]}$] interval $(a,b] \triangleq \{ x \in \set {X} : a < x \leq b \}$|nopage}{100}} \@writefile{symbols}{\indexentry{Csets.2intervals3@[${[a,b)}$] interval $[a,b) \triangleq \{ x \in \set {X} : a \leq x < b \}$|nopage}{100}} \@writefile{symbols}{\indexentry{Csets.2intervals4@[${(a,b)}$] interval $(a,b) \triangleq \{ x \in \set {X} : a < x < b \}$\index {mathematics"!numbers"!real number intervals"|)indexglo}|nopage}{100}} \@writefile{symbols}{\indexentry{Forder.201@[$\sup $] \index {mathematics"!order"!supremum ($\sup $)"|indexglo}supremum (\ie {}, lowest upper bound or join)|nopage}{100}} \@writefile{symbols}{\indexentry{Forder.202@[$\max $] \index {mathematics"!order"!maximum ($\max $)"|indexglo}maximum element|nopage}{100}} \@writefile{symbols}{\indexentry{Forder.201@[$\inf $] \index {mathematics"!order"!infimum ($\inf $)"|indexglo}infimum (\ie {}, greatest lower bound or meet)|nopage}{100}} \@writefile{symbols}{\indexentry{Forder.202@[$\min $] \index {mathematics"!order"!minimum ($\min $)"|indexglo}minimum element|nopage}{100}} \@writefile{symbols}{\indexentry{Dseq.3@[$(x_\alpha )$] a net (\ie {}, an ordered indexed family $(x_\alpha : \alpha \in \set {A})$ with directed index set $\set {A}$)|nopage}{100}} \@writefile{symbols}{\indexentry{Dseq.3@[$(x_n)$] a sequence (\ie {}, an ordered indexed family $(x_n : n \in \N )$ with totally ordered index set $\N $)|nopage}{100}} \@writefile{symbols}{\indexentry{Ageneral.541@[$x + y$] sum of $x$ and $y$|nopage}{100}} \@writefile{symbols}{\indexentry{Ageneral.542@[$x \times y$] product of $x$ and $y$ (also denoted $xy$)|nopage}{100}} \@writefile{symbols}{\indexentry{Ageneral.543@[$-x$] additive inverse of $x$|nopage}{100}} \@writefile{symbols}{\indexentry{Ageneral.5431@[$x - y$] difference of $x$ and $y$ (\ie {}, $x - y \triangleq x + -y$)|nopage}{100}} \@writefile{symbols}{\indexentry{Ageneral.5432@[$\sgn (x)$] sign function of $x$|nopage}{100}} \@writefile{symbols}{\indexentry{Ageneral.5433@[$\pipe x \pipe $] \index {mathematics\"!numbers\"!absolute value\"|indexglo}absolute value of $x$ (\ie {}, $x = \sgn (x) \pipe x \pipe $)|nopage}{100}} \@writefile{symbols}{\indexentry{Ageneral.z@[$\sum $] sum of elements of a set|nopage}{100}} \@writefile{symbols}{\indexentry{Ageneral.z@[$\prod $] product of elements of a set|nopage}{100}} \@writefile{symbols}{\indexentry{Bnumbers.2@[$\W $] the set of the \index {mathematics"!numbers"!whole numbers ($\W $)"|indexglo}whole numbers (\ie {}, $\{0,1,2,3,\dots \}$)|nopage}{100}} \@writefile{symbols}{\indexentry{Bnumbers.1@[$\N $] the set of the \index {mathematics"!numbers"!natural numbers ($\N $)"|indexglo}natural numbers (\ie {}, $\{1,2,3,\dots \}$)|nopage}{100}} \@writefile{symbols}{\indexentry{Bnumbers.3@[$\Z $] the set of the \index {mathematics"!numbers"!integers ($\Z $)"|indexglo}integers (\ie {}, $\{\dots ,-3,-2,-1,0,1,2,3,\dots \}$)|nopage}{100}} \@writefile{symbols}{\indexentry{Bnumbers.4@[$\Q $] the set of the \index {mathematics"!numbers"!rationals ($\Q $)"|indexglo}rationals (\ie {}, ratios of integers)|nopage}{100}} \@writefile{symbols}{\indexentry{Bnumbers.50@[$\R $] the set of the \index {mathematics"!numbers"!real numbers ($\R $)"|indexglo}real numbers|nopage}{100}} \@writefile{symbols}{\indexentry{Bnumbers.510@[$\R _{>0}$] the set of the \index {mathematics"!numbers"!real positive numbers ($\R _{>0}$)"|indexglo}strictly positive real numbers|nopage}{100}} \@writefile{symbols}{\indexentry{Bnumbers.511@[$\R _{\geq 0}$] the set of the \index {mathematics"!numbers"!real non-negative numbers ($\R _{\geq 0}$)"|indexglo}non-negative real numbers|nopage}{100}} \@writefile{symbols}{\indexentry{Bnumbers.520@[$\R _{<0}$] the set of the \index {mathematics"!numbers"!real negative numbers ($\R _{<0}$)"|indexglo}strictly negative real numbers|nopage}{100}} \@writefile{symbols}{\indexentry{Bnumbers.521@[$\R _{\leq 0}$] the set of the \index {mathematics"!numbers"!real non-positive numbers ($\R _{\leq 0}$)"|indexglo}non-positive real numbers|nopage}{100}} \@writefile{symbols}{\indexentry{Bnumbers.53@[$\R _{\neq 0}$] the set of the \index {mathematics"!numbers"!real non-zero numbers ($\R _{\neq 0}$)"|indexglo}non-zero real numbers|nopage}{100}} \@writefile{symbols}{\indexentry{Bnumbers.61@[$\lfloor x \rfloor $] the floor of real number $x$ (\ie {}, the greatest integer not greater than $x$)|nopage}{100}} \@writefile{symbols}{\indexentry{Bnumbers.60@[$\lceil x \rceil $] the ceiling of real number $x$ (\ie {}, the least integer not less than $x$)|nopage}{100}} \@writefile{symbols}{\indexentry{Bnumbers.54@[$\extR $] the set of the \index {mathematics"!numbers"!extended real numbers ($\extR $)"|indexglo}extended real numbers (\ie {}, $\R \cup \{-\infty ,+\infty \}$)|nopage}{100}} \@writefile{symbols}{\indexentry{Ganalysis.120@[$\to $] a limit|nopage}{100}} \@writefile{symbols}{\indexentry{Ganalysis.10@[$\lim $] \index {mathematics"!limit ($\lim $ or $\to $)"|indexglo}limit (\eg {}, unique limit of filter base, function, net, or sequence)|nopage}{100}} \@writefile{symbols}{\indexentry{Ganalysis.122@[$f(x) \to q$] limit of function $f$ (\eg {}, as $x \to p$)|nopage}{100}} \@writefile{symbols}{\indexentry{Ganalysis.121@[$p_n \to p$] limit of sequence $(p_n)$|nopage}{100}} \@writefile{symbols}{\indexentry{Ganalysis.2b@[$f'(x_0)$] the \index {mathematics"!functions"!total derivative ($\total $)"|indexglo}first (total) derivative of function $f$ at point $x_0$|nopage}{100}} \@writefile{symbols}{\indexentry{Ganalysis.2a@[$f'(x_0+)$] the right-hand derivative of function $f$ at point $x_0$|nopage}{100}} \@writefile{symbols}{\indexentry{Ganalysis.2a@[$f'(x_0-)$] the left-hand derivative of function $f$ at point $x_0$|nopage}{100}} \@writefile{symbols}{\indexentry{Ganalysis.2b2@[$f''(x_0)$] the second (ordinary) derivative of function $f$ at point $x_0$|nopage}{100}} \@writefile{symbols}{\indexentry{Ganalysis.2b3@[$f'''(x_0)$] the third (ordinary) derivative of function $f$ at point $x_0$|nopage}{100}} \@writefile{symbols}{\indexentry{Ganalysis.2b4@[$f^{(n)}(x_0)$] the $n\th $ (ordinary) derivative of function $f$ at point $x_0$ where $n \in \{4,5,6,\dots \}$|nopage}{100}} \@writefile{symbols}{\indexentry{Ganalysis.2y@[$\total f/\total t$] total derivative of function $f$ at point $t$|nopage}{100}} \@writefile{symbols}{\indexentry{Ganalysis.2z@[$\partial f/\partial x$] \index {mathematics"!functions"!partial derivative ($\partial $)"|indexglo}partial derivative of function $f$ with respect to $x$|nopage}{100}} \@writefile{symbols}{\indexentry{Ganalysis.2y2@[$\total ^2 f/{\total t}^2$] second total derivative of function $f$ (\ie {}, $f''$)|nopage}{100}} \@writefile{symbols}{\indexentry{Ganalysis.2y3@[$\total ^3 f/{\total t}^3$] third total derivative of function $f$ (\ie {}, $f'''$)|nopage}{100}} \@writefile{symbols}{\indexentry{Ganalysis.2yn@[$\total ^n f/{\total t}^n$] $n\th $ total derivative of function $f$ (\ie {}, $f^{(n)}$)|nopage}{100}} \@writefile{symbols}{\indexentry{Ganalysis.2zxy@[$\partial ^2 f/\partial x \partial y$] partial derivative of function $\partial f/\partial x$ with respect to $y$|nopage}{100}} \@writefile{symbols}{\indexentry{Bnumbers.55@[$e$] \aimention {Leonhard Euler}Euler's number (\ie {}, constant $e \approx 2.71828182845904523536$)|nopage}{100}} \@writefile{symbols}{\indexentry{Ganalysis.001@[${n\bang }$] factorial of $n$ (\ie {}, ${n\bang }=1\times 2\times \cdots \times n$ with ${0\bang }=1$)|nopage}{100}} \@writefile{symbols}{\indexentry{Ageneral.1@[$\approx $] is approximately equal to|nopage}{100}} \@writefile{symbols}{\indexentry{Bnumbers.595@[$\exp (x)$] exponential function (\ie {}, $\exp (x) \triangleq e^x$)|nopage}{100}} \@writefile{symbols}{\indexentry{Bnumbers.58@[$\ln (x)$] natural logarithm of positive real number $x$ (\ie {}, $e^{\ln (x)} = x$)|nopage}{100}} \@writefile{symbols}{\indexentry{Bnumbers.57@[$\log (x)$] common logarithm of positive real number $x$ (\ie {}, $10^{\log (x)} = x$)|nopage}{100}} \@writefile{symbols}{\indexentry{Bnumbers.56@[$\log _b(x)$] logarithm of positive real number $x$ in base $b$ (\ie {}, $b^{\log _b(x)} = x$)|nopage}{100}} \@writefile{symbols}{\indexentry{Hvectors.2@[$y_i$] the $i\th $ coordinate of vector $\v {y}$|nopage}{100}} \@writefile{symbols}{\indexentry{Hvectors.42@[$\v {e}_i$] the $i\th $ elementary (or standard) basis vector|nopage}{100}} \@writefile{symbols}{\indexentry{Hvectors.3@[$\v {x}^\T $] the \index {mathematics"!vector spaces"!vector transpose (${}^\T $)"|indexglo}transpose of vector or covector $\v {x}$ (\ie {}, if $\v {x}$ is an $n$-vector then $\v {x} = [x_1, x_2, \dots , x_n]^\T )$|nopage}{100}} \@writefile{symbols}{\indexentry{Bnumbers.545@[$\R ^n$] the \index {mathematics"!numbers"!Euclidean $n$-space ($\R ^n$)"|indexglo}\aimention {Euclid}Euclidean $n$-space|nopage}{100}} \@writefile{symbols}{\indexentry{Bnumbers.5451@[$\R ^{n \times m}$] space of $n$-by-$m$ real matrices|nopage}{100}} \@writefile{symbols}{\indexentry{Hvectors.31@[$\mat {A}^\T $] the \index {mathematics"!vector spaces"!matrix transpose (${}^\T $)"|indexglo}transpose of matrix $\mat {A}$|nopage}{100}} \@writefile{symbols}{\indexentry{Hvectors.45@[$\I $] the identity matrix|nopage}{100}} \@writefile{symbols}{\indexentry{Bnumbers.5452@[$\R ^{n \times n}$] the unitary associative real algebra|nopage}{100}} \@writefile{symbols}{\indexentry{Hvectors.5@[$\nabla _{\v {x}} f(\v {x})$] the \index {mathematics"!functions"!gradient ($\nabla $)"|indexglo}gradient vector of function $f$ at $\v {x}$|nopage}{100}} \@writefile{symbols}{\indexentry{Hvectors.51@[$\nabla ^2_{\v {x}\v {x}} f(\v {x})$] the \index {mathematics"!functions"!Hessian ($\nabla ^2$)"|indexglo}\aimention {Ludwig Otto Hesse}Hessian matrix of function $f$ at point $\v {x}$|nopage}{100}} \@writefile{symbols}{\indexentry{Iprob.3@[$\Borel (\set {U})$] the \index {mathematics"!sets"!Borel algebra ($\Borel $)"|indexglo}\aimention {\'{E}mile Borel}Borel algebra of set $\set {U}$ (\ie , $\Borel (\set {U})$ is the minimal a $\sigma $-algebra containing the open sets; elements of $\Borel (\set {U})$ are called \emph {\aimention {\'{E}mile Borel}Borel sets} and are subsets of $\set {U}$, so $\Borel (\set {U} \in \Pow (\set {U})$|nopage}{100}} \@writefile{symbols}{\indexentry{Iprob.4@[$\int _a^b f(x) \total x$] the \index {mathematics"!functions"!integral ($\int $)"|indexglo}\aimention {Henri L. Lebesgue}Lebesgue integral of function $f$ over interval $[a,b] \subset \extR $ with respect to the \aimention {Henri L. Lebesgue}Lebesgue measure|nopage}{100}} \@writefile{symbols}{\indexentry{Iprob.5@[$\delta _a(\set {E})$] Dirac delta measure of set $\set {E}$ at point $a$ (\eg {}, $f(0) = \linebreak [4] \int _{-1}^1 f(x) \delta _0(\{x\}) \total x$)|nopage}{100}} \@writefile{symbols}{\indexentry{Iprob.50@[$\delta (x-p)$] Simplified Dirac delta measure notation (\ie {}, $\delta (x-p) \triangleq \delta _p(\{x\})$)|nopage}{100}} \@writefile{symbols}{\indexentry{Iprob.41@[$f * g$] \index {mathematics"!functions"!convolution ($*$)"|indexglo}convolution of function $f$ with function $g$ (\ie {}, $(f * g)(t) \triangleq \int _{-\infty }^\infty f(\tau ) g(t-\tau ) \total \tau $)|nopage}{100}} \@writefile{symbols}{\indexentry{Iprob.541@[$(\set {U},\Sigma ,\Pr )$] \index {stochasticity"!probability space"|indexglo}Probability space with outcomes $\set {U}$, $\sigma $-field of events $\Sigma $, and probability measure $\Pr $|nopage}{100}} \@writefile{symbols}{\indexentry{Iprob.540@[$\Pr $] \index {stochasticity"!probability measure"|indexglo}Probability measure|nopage}{100}} \@writefile{symbols}{\indexentry{Iprob.545@[$\{X \leq a\}$] Measurable set induced by preimage of random variable $X$ (\ie {}, \linebreak [3] $\{ \zeta \in \set {U} : X(\zeta ) \leq a \}$)|nopage}{100}} \@writefile{symbols}{\indexentry{Iprob.546@[$\Pr (X \leq a)$] Probability induced by preimage of random variable $X$ (\ie {}, \linebreak [3] $\Pr (\{ \zeta \in \set {U} : X(\zeta ) \leq a \})$)|nopage}{100}} \@writefile{symbols}{\indexentry{Iprob.55@[$F_X(x)$] \index {stochasticity"!random variable"!cumulative distribution function ($F$)"|indexglo}Cumulative distribution function for random variable $X$ (\ie {}, $F_X(a) \triangleq \Pr (X \leq a)$)|nopage}{100}} \@writefile{symbols}{\indexentry{Iprob.56@[$f_X(x)$] \index {stochasticity"!random variable"!probability density function ($f$)"|indexglo}Probability density function for random variable $X$ (\ie {}, $F_X(a) = \int _{-\infty }^a f_X(x) \total x$)|nopage}{100}} \@writefile{symbols}{\indexentry{Iprob.61@[$\E (g(X))$] \index {stochasticity"!statistics"!expectation of function"|indexglo}Expectation of function $g$ of random variable $X$ (\ie {}, \linebreak [4] $\int _{-\infty }^\infty g(x) f_X(x) \total x$)|nopage}{100}} \@writefile{symbols}{\indexentry{Iprob.60@[$\E (X)$] \index {stochasticity"!statistics"!expectation ($\E $)"|indexglo}Expectation of random variable $X$ (\ie {}, \linebreak [4] $\int _{-\infty }^\infty x f_X(x) \total x$)|nopage}{100}} \@writefile{symbols}{\indexentry{Iprob.62@[$\var (X)$] \index {stochasticity"!statistics"!variance ($\var $)|indexglo}Variance of random variable $X$ (\ie {}, $\var (X) = \E (X^2) - \E (X)^2$)|nopage}{100}} \@writefile{symbols}{\indexentry{Iprob.63@[$\cov (X,Y)$] Covariance of random variables $X$ and $Y$ (\ie {}, $\cov (X,Y) = \E (XY) - \E (X)\E (Y)$)|nopage}{100}} \@writefile{symbols}{\indexentry{Iprob.65@[$F_{XY}(x,y)$] Joint distribution function for random variables $X$ and $Y$ (\ie {}, $F_{XY}(a,b) \triangleq \Pr (X \leq a, Y \leq b)$)|nopage}{100}} \@writefile{symbols}{\indexentry{Iprob.66@[$f_{XY}(x,y)$] Joint density function for random variables $X$ and $Y$|nopage}{100}} \@writefile{symbols}{\indexentry{Iprob.670@[$f_{Y \pipe X}(y \pipe x)$] Conditional density function for random variable $Y$ given $X=x$|nopage}{100}} \@writefile{symbols}{\indexentry{Iprob.671@[$F_{Y \pipe X}(y \pipe x)$] Conditional distribution function for random variable $Y$ given $X=x$|nopage}{100}} \@writefile{symbols}{\indexentry{Iprob.68@[$\E (Y \pipe X)$] \index {stochasticity"!statistics"!conditional expectation"|indexglo}Conditional expectation of $Y$ given $X$|nopage}{100}} \@writefile{symbols}{\indexentry{Iprob.70@[$( \v {N}(t) : t \in \R _{\geq 0})$] \index {stochasticity"!random process"|indexglo}Random process (\ie {}, $\v {N}(t)$ is a random vector for all $t \in \R _{>0}$)|nopage}{100}} \@writefile{symbols}{\indexentry{Iprob.7301@[$Y(t) \xto {a.s.} Y$] \index {stochasticity"!random process"!almost sure limit ($\aslim $ or $\xto {a.s.}$)"|indexglo}Random process $Y(t)$ converges almost surely (\ie {}, $\Pr (\lim _{t \to \infty } Y(t) = Y) = 1$) to $Y$|nopage}{100}} \@writefile{symbols}{\indexentry{Iprob.7303@[$\aslim \limits _{t \to \infty } Y(t) = Y$] Random process $Y(t)$ converges almost surely (\ie {}, with probability 1) to $Y$|nopage}{100}} \newlabel{ch:bibliography}{{A}{100}{Limits of Markov Renewal Processes\relax }{section*.58}{}} \@writefile{toc}{\contentsline {chapter}{Bibliography}{100}{section*.58}} \bibpage{APW04}{\hyperpage{100}} \bibpage{APW06}{\hyperpage{100}} \bibpage{HA99}{\hyperpage{100}} \bibpage{BK95}{\hyperpage{100}} \bibpage{BW96}{\hyperpage{100}} \bibpage{Bawa75}{\hyperpage{100}} \bibpage{Bawa78}{\hyperpage{100}} \bibpage{Bawa82}{\hyperpage{100}} \bibpage{BL77}{\hyperpage{100}} \bibpage{Bertsekas95}{\hyperpage{100}} \aibibcite{Chamberlain83}{13} \bibcite{Chamberlain83}{{13}{1983}{{Chamberlain}}{{}}} \aibibcite{Cha76}{14} \bibcite{Cha76}{{14}{1976{}}{{Charnov}}{{}}} \aibibcite{ChaMantid}{15} \bibcite{ChaMantid}{{15}{1976{}}{{Charnov}}{{}}} \aibibcite{Cha73}{16} \bibcite{Cha73}{{16}{1973}{{Charnov and Orians}}{{}}} \aibibcite{CDHP97}{17} \bibcite{CDHP97}{{17}{1997}{{Chunhachindaa et~al.}}{{Chunhachindaa, Dandapanib, Hamidb, and Prakash}}} \aibibcite{ClkMngl00}{18} \bibcite{ClkMngl00}{{18}{2000}{{Clark and Mangel}}{{}}} \aibibcite{Cody74}{19} \bibcite{Cody74}{{19}{1974}{{Cody}}{{}}} \aibibcite{ES84}{20} \bibcite{ES84}{{20}{1984}{{Engen and Stenseth}}{{}}} \aibibcite{GS83}{21} \bibcite{GS83}{{21}{1983}{{Gendron and Staddon}}{{}}} \aibibcite{GH99}{22} \bibcite{GH99}{{22}{1999}{{Grootveld and Hallerbach}}{{}}} \aibibcite{HR87}{23} \bibcite{HR87}{{23}{1987}{{Harder and Real}}{{}}} \aibibcite{HouMc99}{24} \bibcite{HouMc99}{{24}{1999}{{Houston and McNamara}}{{}}} \aibibcite{Hughes79}{25} \bibcite{Hughes79}{{25}{1979}{{Hughes}}{{}}} \bibpage{Caraco80}{\hyperpage{101}} \bibpage{CB05}{\hyperpage{101}} \bibpage{Chamberlain83}{\hyperpage{101}} \bibpage{Cha76}{\hyperpage{101}} \bibpage{ChaMantid}{\hyperpage{101}} \bibpage{Cha73}{\hyperpage{101}} \bibpage{CDHP97}{\hyperpage{101}} \bibpage{ClkMngl00}{\hyperpage{101}} \bibpage{Cody74}{\hyperpage{101}} \bibpage{ES84}{\hyperpage{101}} \bibpage{GS83}{\hyperpage{101}} \bibpage{GH99}{\hyperpage{101}} \bibpage{HR87}{\hyperpage{101}} \bibpage{HouMc99}{\hyperpage{101}} \aibibcite{HG05}{26} \bibcite{HG05}{{26}{2005}{{Hutchinson and Gigerenzer}}{{}}} \aibibcite{IHY81}{27} \bibcite{IHY81}{{27}{1981}{{Iwasa et~al.}}{{Iwasa, Higashi, and Yamamura}}} \aibibcite{JohnsMiller63}{28} \bibcite{JohnsMiller63}{{28}{1963}{{Johns and Miller}}{{}}} \aibibcite{Kane82}{29} \bibcite{Kane82}{{29}{1982}{{Kane}}{{}}} \aibibcite{KSY93}{30} \bibcite{KSY93}{{30}{1993}{{Konno et~al.}}{{Konno, Shirakawa, and Yamazaki}}} \aibibcite{Lai91}{31} \bibcite{Lai91}{{31}{1991}{{Lai}}{{}}} \aibibcite{LR88}{32} \bibcite{LR88}{{32}{1988}{{Lee and Rao}}{{}}} \aibibcite{Lintner65}{33} \bibcite{Lintner65}{{33}{1965}{{Lintner}}{{}}} \aibibcite{MnglClk88}{34} \bibcite{MnglClk88}{{34}{1988}{{Mangel and Clark}}{{}}} \aibibcite{Mao70}{35} \bibcite{Mao70}{{35}{1970}{{Mao}}{{}}} \aibibcite{Markowitz52}{36} \bibcite{Markowitz52}{{36}{1952}{{Markowitz}}{{}}} \aibibcite{Markowitz59}{37} \bibcite{Markowitz59}{{37}{1959}{{Markowitz}}{{}}} \aibibcite{Marschak46}{38} \bibcite{Marschak46}{{38}{1946}{{Marschak}}{{}}} \aibibcite{McNamara83}{39} \bibcite{McNamara83}{{39}{1983}{{McNamara}}{{}}} \bibpage{Hughes79}{\hyperpage{102}} \bibpage{HG05}{\hyperpage{102}} \bibpage{IHY81}{\hyperpage{102}} \bibpage{JohnsMiller63}{\hyperpage{102}} \bibpage{Kane82}{\hyperpage{102}} \bibpage{KSY93}{\hyperpage{102}} \bibpage{Lai91}{\hyperpage{102}} \bibpage{LR88}{\hyperpage{102}} \bibpage{Lintner65}{\hyperpage{102}} \bibpage{MnglClk88}{\hyperpage{102}} \bibpage{Mao70}{\hyperpage{102}} \bibpage{Markowitz52}{\hyperpage{102}} \bibpage{Markowitz59}{\hyperpage{102}} \aibibcite{Meyer87}{40} \bibcite{Meyer87}{{40}{1987}{{Meyer}}{{}}} \aibibcite{Mossin66}{41} \bibcite{Mossin66}{{41}{1966}{{Mossin}}{{}}} \aibibcite{Murdoch69}{42} \bibcite{Murdoch69}{{42}{1969}{{Murdoch}}{{}}} \aibibcite{Nonacs01}{43} \bibcite{Nonacs01}{{43}{2001}{{Nonacs}}{{}}} \aibibcite{OR83}{44} \bibcite{OR83}{{44}{1983}{{Owen and Rabinovitch}}{{}}} \aibibcite{PapoulisPillai02}{45} \bibcite{PapoulisPillai02}{{45}{2002}{{Papoulis and Pillai}}{{}}} \aibibcite{PP06}{46} \bibcite{PP06}{{46}{}{{Pavlic and Passino}}{{}}} \aibibcite{Pulliam74}{47} \bibcite{Pulliam74}{{47}{1974}{{Pulliam}}{{}}} \aibibcite{Pulliam75}{48} \bibcite{Pulliam75}{{48}{1975}{{Pulliam}}{{}}} \aibibcite{PPC77}{49} \bibcite{PPC77}{{49}{1977}{{Pyke et~al.}}{{Pyke, Pulliam, and Charnov}}} \aibibcite{QAP06}{50} \bibcite{QAP06}{{50}{}{{Quijano et~al.}}{{Quijano, Andrews, and Passino}}} \aibibcite{Rapport71}{51} \bibcite{Rapport71}{{51}{1971}{{Rapport}}{{}}} \aibibcite{Real80}{52} \bibcite{Real80}{{52}{1980}{{Real}}{{}}} \aibibcite{RF94}{53} \bibcite{RF94}{{53}{1994}{{Rom and Ferguson}}{{}}} \bibpage{Marschak46}{\hyperpage{103}} \bibpage{McNamara83}{\hyperpage{103}} \bibpage{Meyer87}{\hyperpage{103}} \bibpage{Mossin66}{\hyperpage{103}} \bibpage{Murdoch69}{\hyperpage{103}} \bibpage{Nonacs01}{\hyperpage{103}} \bibpage{OR83}{\hyperpage{103}} \bibpage{PapoulisPillai02}{\hyperpage{103}} \bibpage{PP06}{\hyperpage{103}} \bibpage{Pulliam74}{\hyperpage{103}} \bibpage{Pulliam75}{\hyperpage{103}} \bibpage{PPC77}{\hyperpage{103}} \bibpage{QAP06}{\hyperpage{103}} \bibpage{Rapport71}{\hyperpage{103}} \aibibcite{RS70}{54} \bibcite{RS70}{{54}{1970}{{Rothschild and Stiglitz}}{{}}} \aibibcite{Schoener71}{55} \bibcite{Schoener71}{{55}{1971}{{Schoener}}{{}}} \aibibcite{Sharpe64}{56} \bibcite{Sharpe64}{{56}{1964}{{Sharpe}}{{}}} \aibibcite{Sharpe66}{57} \bibcite{Sharpe66}{{57}{1966}{{Sharpe}}{{}}} \aibibcite{Sharpe94}{58} \bibcite{Sharpe94}{{58}{1994}{{Sharpe}}{{}}} \aibibcite{SC82}{59} \bibcite{SC82}{{59}{1982}{{Stephens and Charnov}}{{}}} \aibibcite{SK86}{60} \bibcite{SK86}{{60}{1986}{{Stephens and Krebs}}{{}}} \aibibcite{TL81}{61} \bibcite{TL81}{{61}{1981}{{Templeton and Lawlor}}{{}}} \aibibcite{Tobin58}{62} \bibcite{Tobin58}{{62}{1958}{{Tobin}}{{}}} \aibibcite{Tsiang72}{63} \bibcite{Tsiang72}{{63}{1972}{{Tsiang}}{{}}} \aibibcite{Viniotis98}{64} \bibcite{Viniotis98}{{64}{1998}{{Viniotis}}{{}}} \aibibcite{VNM44}{65} \bibcite{VNM44}{{65}{1944}{{von Neumann and Morgenstern}}{{}}} \aibibcite{WaBeHaBo06}{66} \bibcite{WaBeHaBo06}{{66}{2006}{{Wajnberg et~al.}}{{Wajnberg, Bernhard, Hamelin, and Boivin}}} \bibpage{Real80}{\hyperpage{104}} \bibpage{RF94}{\hyperpage{104}} \bibpage{RS70}{\hyperpage{104}} \bibpage{Schoener71}{\hyperpage{104}} \bibpage{Sharpe64}{\hyperpage{104}} \bibpage{Sharpe66}{\hyperpage{104}} \bibpage{Sharpe94}{\hyperpage{104}} \bibpage{SC82}{\hyperpage{104}} \bibpage{SK86}{\hyperpage{104}} \bibpage{TL81}{\hyperpage{104}} \bibpage{Tobin58}{\hyperpage{104}} \bibpage{Tsiang72}{\hyperpage{104}} \bibpage{Viniotis98}{\hyperpage{104}} \bibpage{VNM44}{\hyperpage{104}} \aibibcite{WH74}{67} \bibcite{WH74}{{67}{1974}{{Werner and Hall}}{{}}} \bibpage{WaBeHaBo06}{\hyperpage{105}} \bibpage{WH74}{\hyperpage{105}} \@writefile{toc}{\contentsline {chapter}{List of Acronyms}{106}{appendix*.61}} \newlabel{ch:acronyms}{{A}{106}{List of Acronyms\footnote {\acronymsfootnote {}}\relax }{appendix*.61}{}} \@writefile{default}{\indexentry{stochasticity!central limit theorem (CLT)|indexglo}{106}} \@writefile{default}{\indexentry{extreme-preference rule (EPR)|indexglo}{106}} \@writefile{default}{\indexentry{finance!stochastic dominance (SD)!first-order (FSD)|indexglo}{106}} \@writefile{default}{\indexentry{stochasticity!random variable!iid@\iid |indexglo}{106}} \@writefile{default}{\indexentry{optimality!KKT conditions|indexglo}{106}} \@writefile{default}{\indexentry{stochasticity!statistics!lower-partial moment (LPM)|indexglo}{106}} \@writefile{default}{\indexentry{stochasticity!statistics!lower-partial variance (LPV)|indexglo}{106}} \@writefile{default}{\indexentry{finance!modern portfolio theory (MPT)|indexglo}{106}} \@writefile{default}{\indexentry{mean-variance analysis (MVA)|indexglo}{106}} \@writefile{default}{\indexentry{marginal value theorem (MVT)|indexglo}{106}} \@writefile{default}{\indexentry{optimal foraging theory|indexglo}{106}} \@writefile{default}{\indexentry{finance!post-modern portfolio theory (PMPT)|indexglo}{106}} \@writefile{default}{\indexentry{finance!stochastic dominance (SD)|indexglo}{106}} \@writefile{default}{\indexentry{finance!stochastic dominance (SD)!third-order (TSD)|indexglo}{106}} \@writefile{default}{\indexentry{solitary agent model!parameters|(indexglo}{106}} \@writefile{toc}{\contentsline {chapter}{List of Terms}{107}{appendix*.63}} \newlabel{ch:terms}{{A}{107}{List of Terms\footnote {\termsfootnote {}}\relax }{appendix*.63}{}} \aiexplicit{Sim\'{e}on-Denis Poisson}{\hyperpage{107}} \aiexplicit{Sim\'{e}on-Denis Poisson}{\hyperpage{107}} \aiexplicit{Andrei A. Markov}{\hyperpage{107}} \aiexplicit{Andrei A. Markov}{\hyperpage{107}} \aiexplicit{Andrei A. Markov}{\hyperpage{107}} \aiexplicit{Andrei A. Markov}{\hyperpage{107}} \aiexplicit{Andrei A. Markov}{\hyperpage{107}} \aiexplicit{Andrei A. Markov}{\hyperpage{107}} \aiexplicit{Andrei A. Markov}{\hyperpage{107}} \aiexplicit{Andrei A. Markov}{\hyperpage{107}} \@writefile{default}{\indexentry{Markov renewal cycle!OFT cycle|indexglo}{108}} \aiexplicit{Andrei A. Markov}{\hyperpage{108}} \aiexplicit{Andrei A. Markov}{\hyperpage{108}} \aiexplicit{Sim\'{e}on-Denis Poisson}{\hyperpage{108}} \aiexplicit{Sim\'{e}on-Denis Poisson}{\hyperpage{108}} \aiexplicit{Andrei A. Markov}{\hyperpage{108}} \aiexplicit{Andrei A. Markov}{\hyperpage{108}} \aiexplicit{Andrei A. Markov}{\hyperpage{108}} \aiexplicit{Andrei A. Markov}{\hyperpage{108}} \aiexplicit{Andrei A. Markov}{\hyperpage{108}} \aiexplicit{Andrei A. Markov}{\hyperpage{108}} \aiexplicit{Andrei A. Markov}{\hyperpage{108}} \aiexplicit{Andrei A. Markov}{\hyperpage{108}} \aiexplicit{Andrei A. Markov}{\hyperpage{108}} \aiexplicit{Andrei A. Markov}{\hyperpage{108}} \@writefile{default}{\indexentry{solitary agent model!parameters|)indexglo}{108}} \@writefile{toc}{\contentsline {chapter}{List of Symbols}{109}{appendix*.65}} \newlabel{ch:symbols}{{A}{109}{List of Symbols\relax }{appendix*.65}{}} \@writefile{default}{\indexentry{mathematics|(indexglo}{109}} \@writefile{default}{\indexentry{mathematics!equality ($=$)|indexglo}{109}} \@writefile{default}{\indexentry{mathematics!definition ($\triangleq $)|indexglo}{109}} \@writefile{default}{\indexentry{mathematics!numbers|(indexglo}{109}} \@writefile{default}{\indexentry{mathematics!numbers!natural numbers ($\N $)|indexglo}{109}} \@writefile{default}{\indexentry{mathematics!numbers!whole numbers ($\W $)|indexglo}{109}} \@writefile{default}{\indexentry{mathematics!numbers!integers ($\Z $)|indexglo}{109}} \@writefile{default}{\indexentry{mathematics!numbers!rationals ($\Q $)|indexglo}{109}} \@writefile{default}{\indexentry{mathematics!numbers!real numbers ($\R $)|indexglo}{109}} \@writefile{default}{\indexentry{mathematics!numbers!real positive numbers ($\R _{>0}$)|indexglo}{109}} \@writefile{default}{\indexentry{mathematics!numbers!real non-negative numbers ($\R _{\geq 0}$)|indexglo}{109}} \@writefile{default}{\indexentry{mathematics!numbers!real negative numbers ($\R _{<0}$)|indexglo}{109}} \@writefile{default}{\indexentry{mathematics!numbers!real non-positive numbers ($\R _{\leq 0}$)|indexglo}{109}} \@writefile{default}{\indexentry{mathematics!numbers!real non-zero numbers ($\R _{\neq 0}$)|indexglo}{109}} \@writefile{default}{\indexentry{mathematics!numbers!extended real numbers ($\extR $)|indexglo}{109}} \@writefile{default}{\indexentry{mathematics!numbers!Euclidean $n$-space ($\R ^n$)|indexglo}{109}} \aiexplicit{Euclid}{\hyperpage{109}} \aiexplicit{Leonhard Euler}{\hyperpage{109}} \@writefile{default}{\indexentry{mathematics!numbers|)indexglo}{110}} \@writefile{default}{\indexentry{mathematics!sets|(indexglo}{110}} \@writefile{default}{\indexentry{mathematics!sets!empty set ($\emptyset $)|indexglo}{110}} \@writefile{default}{\indexentry{mathematics!sets!set element ($\in $)|indexglo}{110}} \@writefile{default}{\indexentry{mathematics!sets!exclusion ($\notin $)|indexglo}{110}} \@writefile{default}{\indexentry{mathematics!sets!superset ($\supseteq $ or $\supset $)|indexglo}{110}} \@writefile{default}{\indexentry{mathematics!sets!subset ($\subseteq $ or $\subset $)|indexglo}{110}} \@writefile{default}{\indexentry{mathematics!sets!power set ($\Pow $)|indexglo}{110}} \@writefile{default}{\indexentry{mathematics!sets!set intersection ($\cap $)|indexglo}{110}} \@writefile{default}{\indexentry{mathematics!sets!set union ($\cup $)|indexglo}{110}} \@writefile{default}{\indexentry{mathematics!sets!set difference ($\setdiff $)|indexglo}{110}} \@writefile{default}{\indexentry{mathematics!sets!set complement (${}^c$)|indexglo}{110}} \@writefile{default}{\indexentry{mathematics!ordered pair|indexglo}{110}} \@writefile{default}{\indexentry{mathematics!n-tuple@$n$-tuple|indexglo}{110}} \@writefile{default}{\indexentry{mathematics!sets!Cartesian product ($\times $)|(indexglo}{110}} \aiexplicit{Ren\'{e} Descartes}{\hyperpage{110}} \aiexplicit{Ren\'{e} Descartes}{\hyperpage{110}} \aiexplicit{Ren\'{e} Descartes}{\hyperpage{110}} \@writefile{default}{\indexentry{mathematics!sets!Cartesian product ($\times $)|)indexglo}{110}} \@writefile{default}{\indexentry{mathematics!numbers!real number intervals|(indexglo}{110}} \@writefile{default}{\indexentry{mathematics!numbers!real number intervals|)indexglo}{111}} \@writefile{default}{\indexentry{mathematics!sets|)indexglo}{111}} \@writefile{default}{\indexentry{mathematics!logic|(indexglo}{111}} \@writefile{default}{\indexentry{mathematics!logic!equivalence ($\iff $)|indexglo}{111}} \@writefile{default}{\indexentry{mathematics!logic!implication ($\implies $)|indexglo}{111}} \@writefile{default}{\indexentry{mathematics!logic|)indexglo}{111}} \@writefile{default}{\indexentry{mathematics!order|(indexglo}{111}} \@writefile{default}{\indexentry{mathematics!order!infimum ($\inf $)|indexglo}{111}} \@writefile{default}{\indexentry{mathematics!order!supremum ($\sup $)|indexglo}{111}} \@writefile{default}{\indexentry{mathematics!order!maximum ($\max $)|indexglo}{111}} \@writefile{default}{\indexentry{mathematics!order!minimum ($\min $)|indexglo}{111}} \@writefile{default}{\indexentry{mathematics!order|)indexglo}{111}} \@writefile{default}{\indexentry{mathematics!functions(|indexglo}{111}} \@writefile{default}{\indexentry{mathematics!functions|indexglo}{111}} \@writefile{default}{\indexentry{mathematics!limit ($\lim $ or $\to $)|indexglo}{111}} \@writefile{default}{\indexentry{mathematics!functions!total derivative ($\total $)|indexglo}{111}} \@writefile{default}{\indexentry{mathematics!functions!partial derivative ($\partial $)|indexglo}{111}} \@writefile{default}{\indexentry{mathematics!functions|)indexglo}{111}} \@writefile{default}{\indexentry{mathematics!vector spaces|(indexglo}{111}} \@writefile{default}{\indexentry{mathematics!vector spaces!vector transpose (${}^\T $)|indexglo}{112}} \@writefile{default}{\indexentry{mathematics!vector spaces!matrix transpose (${}^\T $)|indexglo}{112}} \@writefile{default}{\indexentry{mathematics!functions!gradient ($\nabla $)|indexglo}{112}} \@writefile{default}{\indexentry{mathematics!functions!Hessian ($\nabla ^2$)|indexglo}{112}} \aiexplicit{Ludwig Otto Hesse}{\hyperpage{112}} \@writefile{default}{\indexentry{mathematics!vector spaces|)indexglo}{112}} \@writefile{default}{\indexentry{stochasticity|(indexglo}{112}} \@writefile{default}{\indexentry{mathematics!sets!Borel algebra ($\Borel $)|indexglo}{112}} \aiexplicit{\'{E}mile Borel}{\hyperpage{112}} \aiexplicit{\'{E}mile Borel}{\hyperpage{112}} \@writefile{default}{\indexentry{mathematics!functions!integral ($\int $)|indexglo}{112}} \aiexplicit{Henri L. Lebesgue}{\hyperpage{112}} \aiexplicit{Henri L. Lebesgue}{\hyperpage{112}} \@writefile{default}{\indexentry{mathematics!functions!convolution ($*$)|indexglo}{112}} \@writefile{default}{\indexentry{stochasticity!probability measure|indexglo}{112}} \@writefile{default}{\indexentry{stochasticity!probability space|indexglo}{112}} \@writefile{default}{\indexentry{stochasticity!random variable!cumulative distribution function ($F$)|indexglo}{112}} \@writefile{default}{\indexentry{stochasticity!random variable!probability density function ($f$)|indexglo}{112}} \@writefile{default}{\indexentry{stochasticity!statistics!expectation ($\E $)|indexglo}{112}} \@writefile{default}{\indexentry{stochasticity!statistics!expectation of function|indexglo}{112}} \@writefile{default}{\indexentry{stochasticity!statistics!conditional expectation|indexglo}{113}} \@writefile{default}{\indexentry{stochasticity!random process|indexglo}{113}} \@writefile{default}{\indexentry{stochasticity!random process!almost sure limit ($\aslim $ or $\xto {a.s.}$)|indexglo}{113}} \@writefile{default}{\indexentry{stochasticity|)indexglo}{113}} \@writefile{default}{\indexentry{mathematics|)indexglo}{113}} \newlabel{ch:index}{{A}{114}{Index\footnote {\indexfoottext }\relax }{section*.67}{}} \@writefile{toc}{\contentsline {chapter}{Index}{114}{section*.67}} \newlabel{ch:people}{{A}{121}{People\footnote {\aifoottext }\relax }{section*.69}{}} \@writefile{toc}{\contentsline {chapter}{People}{121}{section*.69}}