PROBLEMS ARE FROM THE TEXT BY CHUNG AND WILLIAMS UNLESS INDICATED OTHERWISE. PLEASE HAND IN THE STARRED PROBLEMS BY THE DUE DATE. HOMEWORK SHOULD BE PLACED IN THE TA HOMEWORK BOX FOR DAVID LIPSHUTZ LOCATED IN THE BASEMENT OF AP&M.

HOMEWORK.

Assignment 1: Problems 1*, 2*, 3*, 4, 5* of Chapter 1. Due Friday, October 12, noon.
Hint for uniform integrability question in problem 2: recall that the Poisson process at time n is a sum of n i.i.d. random variables with finite mean and variance and so the central limit theorem applies.
Solutions to homework 1 are available by clicking here. You will need the password given out in class to access these.

Assignment 2: Problems 4, 7, 10*, 11, 12*, 13* of Chapter 2. Due Friday, October 26, noon.
Solutions to homework 2 are available by clicking here.

Assignment 3: Problems 1, 2*, 3* of Chapter 4 and Problem 2* of Chapter 5. Due Friday, November 9.
Solutions to homework 3 are available by clicking here.

Assignment 4: Problems 8, 9, 10*, 11*, 12*, 13 of Chapter 5 and Problems 4*, 5, 6 of Chapter 6. Due Friday, November 30, noon.

Assignment 5: Problems 1, 4*, 5* from Chapter 10. Problems 3, 4 from Chapter 7 (this chapter features local time and Tanaka's formula which were mentioned when we covered an example of an SDE with a weak but no strong solution. You will probably have to read some more in Chapter 7 to do the problems from that Chapter.) Due Friday, December 7, noon. The following exercise is a good one to try after the lectures are complete: Chapter 9, Exercise 4. (No need to hand it in.)