MATH 505 - Stochastic Analysis I

3 units (fi 6)(FIRST, 3-0-0)

Discrete-time stochastic analysis: Stochastic basis, filtration, stochastic sequences. Absolute continuity of probability measures and conditional expectations. Martingale-like and predictable stochastic sequences. Doob's decomposition. Stopping times and related properties. Uniformly integrable stochastic sequences. Transition from discrete-time to continuous-time stochastic analysis. Introduction to stochastic integration with respect to Brownian motion. Prerequisites: STAT 471 or consent of the Department.

STAT 580 - Stochastic Processes

3 units (fi 6)(EITHER, 3-0-0)

Elements of stochastic processes. Discrete and continuous time Markov Chains; Birth and Death processes. Branching processes. Brownian Motion. General Stationary and Markov processes. Examples. Prerequisite: STAT 471 or consent of Instructor.

MATH 510 - Stochastic Analysis II

3 units (fi 6)(SECOND, 3-0-0)

Continuous semimartingales and quadratic variation. Stochastic integrals for continuous semimartingales. Ito's formula. Change of probability measure (Girsanov transformation). Martingale representation theorem for Brownian filtrations. Stochastic differential equations, diffusions. Introduction to discontinuous semimartingales with emphasis on Poisson processes. Prerequisites: MATH 505 or consent of the Department.