## Math 536 (Probability Theory). Spring 2003

**Instructor:**
Steve Krone
**Office Hours:** M, W 8:30, and by appointment.

**Class Time:** MWF 2:30 - 3:20

**Place:** Shoup 307

**Prerequisite:** Math 535 (measure theory and integration)
**FINAL EXAM:** Tuesday, May 13, 3:30-5:30 in our usual classroom.

**Text:** R. Durrett, *Probability: Theory and Examples*,
2nd Ed., Duxbury

This is a first graduate course in probability, based on measure theory.
The goal is to learn the mathematics needed to model and analyse
random phenomena. Math 451 (undergraduate probability) is not a
prerequisite for the course, but having it will certainly help your
intuition.

Grades will be based on homework (30%), a midterm exam (30%), and
a final exam (40%).

Solutions to homework assignments can be found at
http://www.sci.uidaho.edu/newton.

**Course Outline:**

- Probability spaces and random variables, expected value, independence,
Borel-Cantelli lemma, almost sure convergence, convergence in probability,
weak and stong laws of large numbers.

- Weak convergence, central limit theorems, characteristic functions,
stable and infinitely divisible distributions.

- Conditional expectation, filtrations, martingales, martingale convergence
theorem, optional stopping theorem, Doob's maximal inequality, uniform
integrability, 0-1 laws.

- Other topics as time permits from: ergodic theory,
Brownian motion.

**Additional References**

- David Williams,
*Probability with Martingales*, Cambridge
University Press.

- Kai Lai Chung,
*A Course in Probability Theory*, Academic
Press.