\relax \providecommand\hyper@newdestlabel[2]{} \citation{golub2013matrix} \citation{durrett2019probability} \@writefile{toc}{\contentsline {chapter}{\numberline {1}Introduction.}{5}{chapter.1}\protected@file@percent } \@writefile{lof}{\addvspace {10\p@ }} \@writefile{lot}{\addvspace {10\p@ }} \@writefile{toc}{\contentsline {section}{\numberline {1.1}Notation, Definitions \& Basic notions.}{5}{section.1.1}\protected@file@percent } \@writefile{toc}{\contentsline {subsection}{\numberline {1.1.1}Norms and Inner Product}{5}{subsection.1.1.1}\protected@file@percent } \@writefile{toc}{\contentsline {subsection}{\numberline {1.1.2}Probability Space and Brownian Motion}{6}{subsection.1.1.2}\protected@file@percent } \newlabel{1.9}{{1.1.13}{8}{Strong Solution of Stochastic Differential Equation}{theorem.1.1.13}{}} \newlabel{1.9@cref}{{[definition][13][1,1]1.1.13}{[1][7][]8}} \newlabel{1.5}{{1.1.8}{8}{Strong Solution of Stochastic Differential Equation}{equation.1.1.8}{}} \newlabel{1.5@cref}{{[equation][8][1,1]1.1.8}{[1][8][]8}} \@writefile{toc}{\contentsline {subsection}{\numberline {1.1.3}Lipschitz and Related Notions}{9}{subsection.1.1.3}\protected@file@percent } \newlabel{def:1.13}{{1.1.15}{9}{Globally Lipschitz Function}{theorem.1.1.15}{}} \newlabel{def:1.13@cref}{{[definition][15][1,1]1.1.15}{[1][8][]9}} \citation{da_prato_zabczyk_2002} \newlabel{def:1.14}{{1.1.16}{10}{Locally Lipschitz Function}{theorem.1.1.16}{}} \newlabel{def:1.14@cref}{{[definition][16][1,1]1.1.16}{[1][10][]10}} \@writefile{toc}{\contentsline {subsection}{\numberline {1.1.4}Kolmogorov Equations}{10}{subsection.1.1.4}\protected@file@percent } \newlabel{(1.7)}{{1.1.16}{11}{Kolmogorov Equation}{equation.1.1.16}{}} \newlabel{(1.7)@cref}{{[equation][16][1,1]1.1.16}{[1][10][]11}} \@writefile{toc}{\contentsline {subsection}{\numberline {1.1.5}Linear Algebra Notation and Definitions}{12}{subsection.1.1.5}\protected@file@percent } \newlabel{def:1.1.23}{{1.1.23}{12}{Column, Row, and General Vector Notation}{theorem.1.1.23}{}} \newlabel{def:1.1.23@cref}{{[definition][23][1,1]1.1.23}{[1][12][]12}} \@writefile{toc}{\contentsline {subsection}{\numberline {1.1.6}$O$-type notation and function growth}{13}{subsection.1.1.6}\protected@file@percent } \newlabel{1.1.20.1}{{1.1.26.1}{14}{Bounded functions and $O$-type notation}{corollary.1.1.26.1}{}} \newlabel{1.1.20.1@cref}{{[corollary][1][]1.1.26.1}{[1][14][]14}} \newlabel{1.1.20.2}{{1.1.26.2}{14}{}{corollary.1.1.26.2}{}} \newlabel{1.1.20.2@cref}{{[corollary][2][]1.1.26.2}{[1][14][]14}} \@writefile{toc}{\contentsline {subsection}{\numberline {1.1.7}The Iverson Bracket}{15}{subsection.1.1.7}\protected@file@percent } \@setckpt{Introduction}{ \setcounter{page}{16} \setcounter{equation}{34} \setcounter{enumi}{3} \setcounter{enumii}{0} \setcounter{enumiii}{0} \setcounter{enumiv}{0} \setcounter{footnote}{0} \setcounter{mpfootnote}{0} \setcounter{part}{1} \setcounter{chapter}{1} \setcounter{section}{1} \setcounter{subsection}{7} \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{section@level}{2} \setcounter{Item}{23} \setcounter{Hfootnote}{0} \setcounter{bookmark@seq@number}{10} \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{lstnumber}{1} \setcounter{theorem}{28} \setcounter{corollary}{0} \setcounter{lstlisting}{0} }