\contentsline {chapter}{\numberline {1}Introduction}{4}{chapter.1}%
\contentsline {section}{\numberline {1.1}Notation and Definitions}{4}{section.1.1}%
\contentsline {chapter}{\numberline {2}Brownian Motion Monte Carlo}{10}{chapter.2}%
\contentsline {section}{\numberline {2.1}Brownian Motion Preliminaries}{10}{section.2.1}%
\contentsline {section}{\numberline {2.2}Monte Carlo Approximations}{14}{section.2.2}%
\contentsline {section}{\numberline {2.3}Bounds and Covnvergence}{15}{section.2.3}%
\contentsline {chapter}{\numberline {3}That $u$ is a viscosity solution}{24}{chapter.3}%
\contentsline {section}{\numberline {3.1}Some Preliminaries}{24}{section.3.1}%
\contentsline {section}{\numberline {3.2}Viscosity Solutions}{28}{section.3.2}%
\contentsline {section}{\numberline {3.3}Solutions, characterization, and computational bounds to the Kolmogorov backward equations}{47}{section.3.3}%
\contentsline {chapter}{Appendices}{55}{section*.3}%