The class meets Mondays 5.10-7.00 PM in room 101 ground floor of Warren Weaver Hall.
Prerequsite: G63.2901 Basic Probability or equivalent.
Review of basic probability and useful tools. Bernoulli trials and random walk. Law of large numbers and central limit theorem. Conditional expectation and martingales. Brownian motion and its simplest properties. Diffusion in general: forward and backward Kolmogorov equations, stochastic differential equations and the Ito calculus. Feynman-Kac and Cameron-Martin Formulas. Applications as time permits.
Independent Random variables
Brownian Motion II
Stochastic Differential equations
Connection with PDE
Markov Chain Approximations.
Take Home Final
Brownian Motion on a half space.