dissertation_work/Dissertation/Introduction.aux

73 lines
3.6 KiB
TeX
Raw Normal View History

2024-02-19 17:04:37 +00:00
\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}
}