Subject: STA 235C
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 235B or MAT 235B; or Consent of Instructor.
Cross Listed
Same course as MAT 235C.
Expanded Course Description
Summary of Course Content:
The main focus is invariance principle and properties of Brownian motion. Also, any topics from the Math/STA 235B list, which were not covered in 235B, may be covered in this part. 1. Weak convergence in metric spaces. 2. Brownian motion.
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