\relax \providecommand\zref@newlabel[2]{} \providecommand\hyper@newdestlabel[2]{} \citation{durrett2019probability} \citation{karatzas1991brownian} \@writefile{toc}{\contentsline {chapter}{\numberline {2}Brownian Motion Monte Carlo}{18}{chapter.2}\protected@file@percent } \@writefile{lof}{\addvspace {10\p@ }} \@writefile{lot}{\addvspace {10\p@ }} \@writefile{toc}{\contentsline {section}{\numberline {2.1}Brownian Motion Preliminaries}{18}{section.2.1}\protected@file@percent } \newlabel{iobm}{{2.1.2}{19}{Independence of Brownian Motion}{theorem.2.1.2}{}} \newlabel{iobm@cref}{{[lemma][2][2,1]2.1.2}{[1][19][]19}} \newlabel{def:1.17}{{2.1.5}{21}{Of $\mathfrak {k}$}{theorem.2.1.5}{}} \newlabel{def:1.17@cref}{{[definition][5][2,1]2.1.5}{[1][21][]21}} \newlabel{primarysetting}{{2.1.6}{21}{Primary Setting For This Chapter}{theorem.2.1.6}{}} \newlabel{primarysetting@cref}{{[definition][6][2,1]2.1.6}{[1][21][]21}} \newlabel{(2.1.2)}{{2.3}{21}{Primary Setting For This Chapter}{equation.2.1.3}{}} \newlabel{(2.1.2)@cref}{{[equation][3][2,1]2.3}{[1][21][]21}} \citation{hutzenthaler_overcoming_2020} \newlabel{(1.12)}{{2.4}{22}{Primary Setting For This Chapter}{equation.2.1.4}{}} \newlabel{(1.12)@cref}{{[equation][4][2,1]2.4}{[1][21][]22}} \newlabel{(2.1.4)}{{2.5}{22}{Primary Setting For This Chapter}{equation.2.1.5}{}} \newlabel{(2.1.4)@cref}{{[equation][5][2,1]2.5}{[1][22][]22}} \newlabel{lemma1.1}{{2.1.7}{22}{}{theorem.2.1.7}{}} \newlabel{lemma1.1@cref}{{[lemma][7][2,1]2.1.7}{[1][22][]22}} \newlabel{lem:1.20}{{2.1.8}{23}{}{theorem.2.1.8}{}} \newlabel{lem:1.20@cref}{{[lemma][8][2,1]2.1.8}{[1][23][]23}} \newlabel{(2.1.6)}{{2.7}{23}{Brownian Motion Preliminaries}{equation.2.1.7}{}} \newlabel{(2.1.6)@cref}{{[equation][7][2,1]2.7}{[1][23][]23}} \newlabel{eq:1.4}{{2.1}{23}{Brownian Motion Preliminaries}{equation.2.1.7}{}} \newlabel{eq:1.4@cref}{{[section][1][2]2.1}{[1][23][]23}} \newlabel{(1.17)}{{2.8}{23}{Brownian Motion Preliminaries}{equation.2.1.8}{}} \newlabel{(1.17)@cref}{{[equation][8][2,1]2.8}{[1][23][]23}} \newlabel{(1.18)}{{2.9}{23}{Brownian Motion Preliminaries}{equation.2.1.9}{}} \newlabel{(1.18)@cref}{{[equation][9][2,1]2.9}{[1][23][]23}} \newlabel{(1.19)}{{2.10}{23}{Brownian Motion Preliminaries}{equation.2.1.10}{}} \newlabel{(1.19)@cref}{{[equation][10][2,1]2.10}{[1][23][]23}} \newlabel{(1.20)}{{2.11}{24}{Brownian Motion Preliminaries}{equation.2.1.11}{}} \newlabel{(1.20)@cref}{{[equation][11][2,1]2.11}{[1][24][]24}} \newlabel{(1.21)}{{2.12}{24}{Brownian Motion Preliminaries}{equation.2.1.12}{}} \newlabel{(1.21)@cref}{{[equation][12][2,1]2.12}{[1][24][]24}} \newlabel{cor:1.20.1}{{2.1.8.1}{24}{}{corollary.2.1.8.1}{}} \newlabel{cor:1.20.1@cref}{{[corollary][1][]2.1.8.1}{[1][24][]24}} \citation{rio_moment_2009} \citation{rio_moment_2009} \@writefile{toc}{\contentsline {section}{\numberline {2.2}Monte Carlo Approximations}{25}{section.2.2}\protected@file@percent } \newlabel{lem:1.21}{{2.2.1}{25}{}{theorem.2.2.1}{}} \newlabel{lem:1.21@cref}{{[lemma][1][2,2]2.2.1}{[1][24][]25}} \newlabel{corollary:1.11.1.}{{2.2.1.1}{25}{}{corollary.2.2.1.1}{}} \newlabel{corollary:1.11.1.@cref}{{[corollary][1][]2.2.1.1}{[1][25][]25}} \citation{grohsetal} \newlabel{(1.26)}{{2.5}{26}{}{equation.2.2.5}{}} \newlabel{(1.26)@cref}{{[equation][5][2,2]2.5}{[1][25][]26}} \newlabel{cor:1.22.2}{{2.2.1.2}{26}{}{corollary.2.2.1.2}{}} \newlabel{cor:1.22.2@cref}{{[corollary][2][]2.2.1.2}{[1][26][]26}} \@writefile{toc}{\contentsline {section}{\numberline {2.3}Bounds and Covnvergence}{26}{section.2.3}\protected@file@percent } \newlabel{lem:1.21}{{2.3.1}{26}{}{theorem.2.3.1}{}} \newlabel{lem:1.21@cref}{{[lemma][1][2,3]2.3.1}{[1][26][]26}} \newlabel{lem:1.22}{{2.3.2}{27}{}{theorem.2.3.2}{}} \newlabel{lem:1.22@cref}{{[lemma][2][2,3]2.3.2}{[1][27][]27}} \newlabel{lem:1.25}{{2.3.3}{28}{}{theorem.2.3.3}{}} \newlabel{lem:1.25@cref}{{[lemma][3][2,3]2.3.3}{[1][28][]28}} \newlabel{(1.46)}{{2.16}{29}{Bounds and Covnvergence}{equation.2.3.16}{}} \newlabel{(1.46)@cref}{{[equation][16][2,3]2.16}{[1][29][]29}} \newlabel{(1.47)}{{2.17}{29}{Bounds and Covnvergence}{equation.2.3.17}{}} \newlabel{(1.47)@cref}{{[equation][17][2,3]2.17}{[1][29][]29}} \newlabel{(1.48)}{{2.18}{29}{Bounds and Covnvergence}{equation.2.3.18}{}} \newlabel{(1.48)@cref}{{[equation][18][2,3]2.18}{[1][29][]29}} \newlabel{cor:1.25.1}{{2.3.3.1}{29}{}{corollary.2.3.3.1}{}} \newlabel{cor:1.25.1@cref}{{[corollary][1][]2.3.3.1}{[1][29][]29}} \newlabel{tentpole_1}{{2.3.4}{30}{}{theorem.2.3.4}{}} \newlabel{tentpole_1@cref}{{[theorem][4][2,3]2.3.4}{[1][30][]30}} \newlabel{(2.48)}{{2.26}{31}{}{equation.2.3.26}{}} \newlabel{(2.48)@cref}{{[equation][26][2,3]2.26}{[1][31][]31}} \newlabel{2.3.27}{{2.27}{31}{}{equation.2.3.27}{}} \newlabel{2.3.27@cref}{{[equation][27][2,3]2.27}{[1][31][]31}} \citation{hjw2020} \citation{hjw2020} \citation{hjw2020} \newlabel{2.3.29}{{2.28}{32}{Bounds and Covnvergence}{equation.2.3.28}{}} \newlabel{2.3.29@cref}{{[equation][28][2,3]2.28}{[1][31][]32}} \newlabel{(2.3.33)}{{2.33}{34}{Bounds and Covnvergence}{equation.2.3.33}{}} \newlabel{(2.3.33)@cref}{{[equation][33][2,3]2.33}{[1][33][]34}} \newlabel{2.3.34}{{2.34}{34}{Bounds and Covnvergence}{equation.2.3.34}{}} \newlabel{2.3.34@cref}{{[equation][34][2,3]2.34}{[1][34][]34}} \newlabel{(2.3.35)}{{2.35}{34}{Bounds and Covnvergence}{equation.2.3.35}{}} \newlabel{(2.3.35)@cref}{{[equation][35][2,3]2.35}{[1][34][]34}} \@setckpt{Brownian_motion_monte_carlo}{ \setcounter{page}{35} \setcounter{equation}{36} \setcounter{enumi}{2} \setcounter{enumii}{0} \setcounter{enumiii}{0} \setcounter{enumiv}{0} \setcounter{footnote}{0} \setcounter{mpfootnote}{0} \setcounter{part}{1} \setcounter{chapter}{2} \setcounter{section}{3} \setcounter{subsection}{0} \setcounter{subsubsection}{0} \setcounter{paragraph}{0} \setcounter{subparagraph}{0} \setcounter{figure}{0} \setcounter{table}{0} \setcounter{@pps}{0} \setcounter{@ppsavesec}{0} \setcounter{@ppsaveapp}{0} \setcounter{AM@survey}{0} \setcounter{parentequation}{0} \setcounter{footdir@label}{0} \setcounter{tmpA}{0} \setcounter{tmpB}{0} \setcounter{tmpC}{0} \setcounter{tmpD}{0} \setcounter{tmpE}{0} \setcounter{tmpF}{0} \setcounter{Hijriday}{0} \setcounter{Hijrimonth}{0} \setcounter{Hijriyear}{0} \setcounter{subfigure}{0} \setcounter{lofdepth}{1} \setcounter{subtable}{0} \setcounter{lotdepth}{1} \setcounter{section@level}{1} \setcounter{Item}{35} \setcounter{Hfootnote}{0} \setcounter{Hy@AnnotLevel}{0} \setcounter{bookmark@seq@number}{15} \setcounter{NAT@ctr}{0} \setcounter{ALG@line}{0} \setcounter{ALG@rem}{0} \setcounter{ALG@nested}{0} \setcounter{ALG@Lnr}{1} \setcounter{ALG@blocknr}{1} \setcounter{ALG@storecount}{0} \setcounter{ALG@tmpcounter}{0} \setcounter{@stackindex}{0} \setcounter{ROWcellindex@}{0} \setcounter{lstnumber}{1} \setcounter{theorem}{4} \setcounter{corollary}{0} \setcounter{lstlisting}{0} }