Instructor: Christopher Hoffman, Padelford C-419,
hoffman at math dot washington dot edu
Lectures: Mon,Wed,Fri 11:30-12:20, JHN 022
Office Hours: Mon 10-11:20 and by appointment
Final Exam: Wed Dec 10, 2:30-4:20, JHN 022
Grading: Homework (50%), Final Exam (40%), Presentations (10%)
Prerequisite: Math 426 or 524 (Measure Theory) is recommended
1. Review of Measure Theory
2. Borel-Cantelli lemmas
3. Laws of Large numbers and concentration for sums of independent bounded random variables
4. Modes of convergence
5. Simple random walk and Gamblers Ruin
6. Kolmogorov and Hewitt-Savage zero-one laws
7. Product measure and Fubini's theorem
8. Exponential random variables and Poisson processes
9. Gaussian random variables and Lindeberg's proof of the central limit theorem
10. Markov chains: stationary distributions, recurrence and transience
11. Kolmogorov extension theorem
12. Martingales and conditional expectation
Math 522 is the continuation of this course, and will cover topics from Chapters 4,5,6,7 of Durrett's text.
Measure theory background: G. B. Folland: Real Analysis: Modern Techniques and Their Applications. Wiley.
Advanced undergraduate probability: G. R. Grimmett and D. R. Stirzaker: Probability and Random Processes, Oxford.
Very advanced and concise reference: O. Kallenberg. Foundations of Modern Probability.
Other relevant books:
D. Williams. Probability with Martingales
L. Breiman. Probability. SIAM.
P. Billingsley. Probability and Measure.
K.L. Chung. A course in probability theory.
D.W. Stroock. Probability Theory: an analytic view.
A. Gut. Probability: A Graduate Course. Springer.
G.R. Grimmett. Percolation. Springer.