Course: STAT 902 - Theory of Probability 2
Blurb:
A rigorous introduction to Brownian motion and stochastic calculus. Topics will include:
Brownian Motion and its constructions, white noise, stochastic calculus, stochastic differential
equations (including solution theory and connections to partial differential equations), functional
limit theory, the general theory of Markov processes (including the Martingale problem and
semigroup theory). Depending on time and interest we may cover: stochastic integration for
semimartingales, the Dambis-Dubbins-Schwarz theorem, Local times, Ito-to-Stratonovich
corrections, the Wong-Zakai approximation, stochastic partial differential equations.
Official Pre-requisites: None
Suggested Pre-requisites: Strong comfort with measure theory or measure theoretic probability is required,
exposure to the material in Stat 901 will be assumed. Some exposure to function spaces will not
be assumed but will definitely help. If you are concerned about your analysis background, please
get in touch and I can make some suggestions. The book “Real Analysis for Graduate Students”
by Bass—available for free from his website—is a fantastic resource.
Course Notes