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Instructor Class Description

Time Schedule:

Soumik Pal
STAT 522
Seattle Campus

Advanced Probability

Measure theory and integration, independence, laws of large numbers. Fourier analysis of distributions, central limit problem and infinitely divisible laws, conditional expectations, martingales. Prerequisite: either MATH 426 or MATH 576. Offered: jointly with MATH 522; W.

Class description

Instruction period: Jan 3 -- Mar 11

Week 1: Weak convergence on metric spaces. Week 2: Construction of Brownian motion, Donsker's invariance. Week 3: Basic properties of Brownian motion. Week 4: Continuous (local) martingales. Week 5: Stochastic integration with respect to Brownian motion. Week 6: Ito's formula for Brownian motion. Week 7: Markov processes. Strong Markov property. Week 8: Brownian motion as a strong Markov process. Week 9: Dirichlet problem. Feynman-Kac formula. Week 10: General Gaussian processes.

Student learning goals

General method of instruction

Recommended preparation

Class assignments and grading

The information above is intended to be helpful in choosing courses. Because the instructor may further develop his/her plans for this course, its characteristics are subject to change without notice. In most cases, the official course syllabus will be distributed on the first day of class.
Last Update by Soumik Pal
Date: 11/16/2010