Subject: STA 235B
Title: Probability Theory
Units 4.0
School: College of Letters and Science LS
Department: Statistics STA
Effective Term: 2008 Spring
Learning Activities
- Lecture - 3.0 hours
- Term Paper/Discussion - 1.0 hours
Description
Measure-theoretic foundations, abstract integration, independence, laws of large numbers, characteristic functions, central limit theorems. Weak convergence in metric spaces, Brownian motion, invariance principle. Conditional expectation. Topics selected from: martingales, Markov chains, ergodic theory.
Prerequisites
STA 235A or MAT 235A; or Consent of Instructor.
Cross Listed
Same course as MAt 235B.
Expanded Course Description
Summary of Course Content:
This part focuses on non-independent stochastic sequences. 1. Radon-Nikodym theorem and conditional expectation. The remaining topics can be chosen from the following list: A. Martingales. B. Ergodic theory C. Markov Chains.
Illustrative Reading:
The book used for the entire sequence is R. Durrett, `Probability and Examples, 2nd Edition, 1996.' Other books are used to provide for additional reading material, such as D. Williams, `
Probability with Martingales,' 1991.
Potential Course Overlap:
None