MTH 287/STA 207, Fall 2000
Probability --- Brownian Motion and Stochastic Calculus  
MW 2:20 -- 3:35 , 218 Physics
Greg Lawler, 128B Physics

Office Hours: Tuesday, 1:30 --3:30 and by appointment

This course will be an introduction to Brownian motion and stochastic calculus. The course will start with a quick discussion of the tools of measure theoretic probability needed to study Brownian motion and stochastic calculus and then will proceed to study these processes from a mathematically rigorous perspective. In the later part of the course I will give an introduction to two other models: fractional Brownian motion and stable processes. The prerequisite for this course is a course in measure theory --- either Math 241 or Stat 205. It will be useful if students have some background in measure theoretic probability --- here are some notes that I used in Math 241 in Fall 1999 on probability. For a reference on other facts use, a (relatively) inexpensive introduction to measure theoretic probability is Williams, Probability with Martingales. This course will not follow the description of Math 287 in the catalogue. There is very little overlap with either Math 241 or Stat 205.

Text

Karatzas and Shreve, Brownian Motion and Stochastic Calculus

Homework

Occasional HW assignments will be given in the lectures. Solutions to problems assigned a particular week should be handed in on Wednesday of the following week. I will keep track here of which problems are due.

PS1 (due 9/6): Chapter 1, 1.5 and the following problem: If X is a random variable then the collection of events that are inverse images of Borel sets is a sigma-algebra.
PS2 (due 9/13)
PS3 (due 9/20)
PS4 (due 9/27)
PS5 (due 10/4)
PS6 (due 10/18)
PS7 (due 11/1) Chapter 3: 3.10, 3.17, 3.18

Problem Set 8 . This is a final problem set and is due by Friday, December 15 at 10:00 am. You can return it (during business hours) to my mailbox in Room 121, Physics.

Extra Notes

Here will be extra notes on material from class.

Constructing Brownian motion (posted Sept. 18)

Last modified: 27 November 00