Subject: STA 235A
Title: Probability Theory
Units: 4.0
School: College of Letters and Science LS
Department: Statistics STA
Effective Term: 2007 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
(MAT 125B, MAT 135A) or STA 131A; or Consent of Instructor.
Cross Listed
Same course as MAT 235A.
Expanded Course Description
Summary of Course Content:
The basic aim of this part of the course is limit theorems for sums of i.i.d. random variables.
1. Basic measure theoretical setting (sigma fields, measures, extensions), random variables, distributions, expected values, moments, convergence theorems, product measures and independence. 2. Weak and strong laws of large numbers. 3. Convergence in distribution and central limit theorems. 4. Special topics: Poisson convergence and/or large deviations.
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