Statistics 251b/551b (Spring 2004)

Stochastic Processes

A study of random processes, including Markov chains, Markov random fields, martingales, random walks, Brownian motion and diffusions. Introduction to certain modern techniques in probability such as coupling and large deviations. Applications to image reconstruction, Bayesian statistics, finance, probabilistic analysis of algorithms, genetics and evolution. After Statistics 241a or equivalent.

Instructor: David Pollard (24 Hillhouse Avenue;
Office hours: Tuesdays 11:00 -- 12:00, or by appointment

TA: Anna Kotchetkova
Office hours: TBA

Lectures: Monday, Wednesday 1:00 - 2:15

Where: 102 Becton center (15 Prospect St)


A knowlege of elementary probability theory at the level of Statistics 241. See some of my notes from 241 for a brief summary of facts about conditional probabilities and conditional expectations.


The course will be based on a book manuscript being prepared by Joe Chang [table of contents]. I will take some material from each chapter. I will post supplementary notes if I deviate too far from Joe's treatment of any topic.


homework and solutions


Week by week

Week starting Monday Wednesday Homework
12 Jan Overview. Read JC §1.1, §1.2 Some examples of MCs.
19 Jan Classification of states Stationary distributions #1 due ??
26 Jan Behavior of a MC during a cycle Positive recurrence
2 Feb Basic limit theorem The Metropolis method
9 Feb Simulated annealing ... ... continued
16 Feb Card shuffling Martingales
23 Feb Optional sampling of martingales Option pricing in discrete time
1 Mar Convergence of positive supermartingales Branching processes
8 & 15 Mar spring break
22 Mar Brownian motion Reflection principle; Ornstein-Uhlenbeck
29 Mar Sample paths of Brownian motion; quadratic variation; diffusions Ito stochastic integral
5 Apr
12 Apr
19 Apr

DBP 6jan04