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:

  1. Probability spaces and random variables, expected value, independence, Borel-Cantelli lemma, almost sure convergence, convergence in probability, weak and stong laws of large numbers.
  2. Weak convergence, central limit theorems, characteristic functions, stable and infinitely divisible distributions.
  3. Conditional expectation, filtrations, martingales, martingale convergence theorem, optional stopping theorem, Doob's maximal inequality, uniform integrability, 0-1 laws.
  4. Other topics as time permits from: ergodic theory, Brownian motion.

Additional References