This article is the index for STA447 materials on Undertide. It collects the generated stochastic-process map and supporting articles on martingales, optional stopping, Brownian motion, and Ito calculus.
Core Notes
STA447 Stochastic Process MOC
The generated map of content for Markov chains, martingales, stopping times, Brownian motion, Ito integrals, quadratic variation, and related advanced topics.
Brownian Motion and Ito Calculus
Brownian Motion
Definitions, Gaussian-process view, martingale properties, continuous-time optional stopping, and reflection principle.
Ito Calculus
Ito-calculus rules, Ito-integral properties, quadratic variation, and common problem templates.
Martingales and Optional Stopping
Doob’s Maximal Inequality
Doob maximal inequality and its connection with uniform integrability, Lp boundedness, and martingale convergence.
Martingale Convergence Theorem
MCT, nonnegative martingales, uniform integrability, and common sufficient conditions.
Optional Stopping Time: Gambler’s Ruin Problem
Using the optional stopping theorem to solve gambler’s ruin hitting probability.