Spring 2014

Instructor: Professor Steve Lalley

Office: 118 Eckhart Hall

Office Hour: Thursday 1:00 - 2:00

Phone: 702-9890

E-mail:
`lalley@galton.uchicago.edu`

This course is the second of a three-quarter sequence in measure-theoretic probability. It is meant for students with a solid grounding in real analysis, including measure and integration, at the level of Stat 381 or Math 312. The main topics to be covered (not necessarily in the order listed) will be :

- Hilbert space and the Radon-Nikodym Theorem (1 week)
- Conditional Probability and Expectation (2 weeks)
- Discrete-Time Martingales (2 weeks)
- Concentration Inequalities (1 week)
- Random Walks (2 weeks)
- Brownian Motion (2 weeks)

There will be weekly homework and a final exam.

- Probability and Measure by Patrick Billingsley
- Probability with Martingales by David Williams

- Hilbert Spaces and the Radon-Nikodym Theorem
- Conditional Expectation
- Martingales Corrected April 25 2017
- Ergodic Theorems
- Renewal Theory
- Lindeberg's Method and the Martingale Central Limit Theorem
- Introduction to Concentration Inequalities
- Large Deviations, Exponential Families, and Cramer's Theorem

- Assignment 1 Due: Monday April 7
- Assignment 2 Due: Monday April 14 Corrected April 7, 4:18 p.m.
- Assignment 3 Due: Monday April 21
- Assignment 4 Due: Monday April 28
- Assignment 5 Due: Monday May 5
- Assignment 6 Due: Monday May 12
- Assignment 8 Due: Friday May 30