Math 5040: Stochastic Processes and Simulation I, Fall 2009



Time and place: 9:40--10:30 MWF in JWB 308.

Instructor: S. Ethier (Prof.), JWB 119, 581-6148, ethier@math.utah.edu. Office hours are 11--12 MWF unless announced otherwise. Other times are available by appointment.

Text: Introduction to Stochastic Processes, Second Edition by Gregory F. Lawler (Chapman & Hall/CRC, 2006). Available at amazon for $58.95.

Prerequisite: Math 5010. This is absolutely essential. Also, some knowledge of computer programming will be helpful.

Topics covered: We will cover the whole book over the course of two semesters. This will probably require supplementing the material in the book. But we will begin with some lectures on simulation, which the book does not cover. For that material a good reference is Sheldon Ross's Introduction to Probability Models, Chapter 11. This book will be on 3-hour reserve in the Marriott Library, and I will post lecture notes on this web page, at least for the simulation material.

Assignments: There will be textbook assignments and simulation assignments. For the simulation assignments, you can use whatever programming language you prefer (C++, FORTRAN, Pascal, BASIC, Excel, Mathematica, MatLab, Maple, Java, R, etc.). You will turn in your program (with documentation, i.e., comments explaining what your instructions mean) and output on paper. I do not want an electronic file. The purpose of the assignments is to learn the material. Therefore, working in groups is not allowed because the result is usually that one person does the work and the others copy it. Evidence of collaboration or plagiarism will result in severe penalties for all involved.

Grades: There will be a midterm exam shortly after Fall Break. There will be a final exam on Thursday, December 17 at 8 a.m. Grades will be based on homework (30%), simulation assignments (20%), midterm exam (20%), and final exam (30%). Lectures 1-6, through Sept. 4.
Assignment 1. Suggested solutions.
Assignment 2. Chapter 1: 5, 8, 10, 14, 17, 19. Also, first solve 17 with N=5 by computer simulation. Due Fri., Oct. 9. Solutions.
Assignment 3. Deadline changed to Friday, Nov. 6. Solutions are available---see instructor for URL.
Assignment 4.

Midterm Exam is scheduled for Friday, Oct. 23. It will be based on simulation and finite Markov chains. Solutions.

Programs for optimal stopping algorithm here.