Course: MATH 171, Stochastic Processes, Winter 2017
Prerequisite: Math 33A and Math 170A (or Statistics 100A). It is helpful, though not required, to take Math 170B before this course or concurrently with this course.
Course Content: A stochastic process is a collection of random variables. These random variables are often indexed by time, and the random variables are often related to each other by the evolution of some physical procedure. Stochastic processes can then model random phenomena that depend on time. We will study Markov chains, Martingales, Poisson Processes, Renewal Processes, and Brownian Motion
Last update: 22 March 2017

Instructor: Steven Heilman, heilman(@-symbol)
Office Hours: Fridays, 830AM-1030AM, MS 5634
Lecture Meeting Time/Location: Monday, Wednesday and Friday, 11AM-1150AM, MS 5117
TA:Yuming Zhang, yzhangpaul(@-symbol)
TA Office Hours: Tuesdays 10AM-11AM, Fridays 2PM-3PM, MS 6153
Discussion Session Meeting Time/Location: Tuesdays, 11AM-1150AM, MS 5117
Required Textbook: Rick Durrett, Essentials of Stochastic Processes, 2nd edition. (The book is freely available online).
Other Textbooks (not required): Markov Chains and Mixing Times, Levin, Peres and Wilmer. (This book is freely available online; see also the errata.) This book is a bit more comprehensive and a bit more advanced in the topics that are covered, but I still highly recommend it. It also focuses more on Markov Chains.
First Midterm: Friday, February 3, 11AM-1150AM, Perloff 1102
Second Midterm: Monday, February 27, 11AM-1150AM, Royce 190
Final Exam: Friday, March 24, 3PM-6PM, MS 5117
Other Resources: An introduction to mathematical arguments, Michael Hutchings, An Introduction to Proofs, How to Write Mathematical Arguments
Email Policy:

Exam Procedures: Students must bring their UCLA ID cards to the midterms and to the final exam. Phones must be turned off. Cheating on an exam results in a score of zero on that exam. Exams can be regraded at most 15 days after the date of the exam. This policy extends to homeworks as well. All students are expected to be familiar with the UCLA Student Guide to Academic Integrity. If you are an OSD student, I would encourage you to discuss with me ways that I can improve your learning experience; I would also encourage you to contact the OSD office to confirm your exam arrangements at the beginning of the quarter.
Exam Resources: Here are the exams and solutions from last quarter's 171 class: Exam 1 Exam 1 Solutions Exam 2 Exam 2 Solutions Final Final Solutions. Here is a page containing practice exams for another 171 class. Here is a page containing practice exams for a class similar to a 171 class. Here is a page containing practice exams for a class similar to a 171 class. Occasionally these exams will cover slightly different material than this class, or the material will be in a slightly different order, but generally, the concepts should be close if not identical.

Homework Policy: Grading Policy:

Tentative Schedule: (This schedule may change slightly during the course.)

Week Monday Tuesday Wednesday Thursday Friday
1 Jan 9: A.1, A.2, Review of Probability Jan 10: Homework 0 (ungraded) Jan 11: A.3, Review; Law of Large Numbers Jan 13: Central Limit Theorem
2 Jan 16: No class Jan 17: Homework 1 due Jan 18: 1.1, Markov Chains Jan 20: 1.1, Examples of Markov Chains
3 Jan 23: 1.3, Classification of States Jan 24: Homework 2 due Jan 25: 1.4, Stationary Distributions Jan 27: 1.5, Limiting Behavior
4 Jan 30: 1.7, Proofs of Limiting Behavior Jan 31: Homework 3 due Feb 1: 1.7, Proofs of Limiting Behavior Feb 3: Midterm #1
5 Feb 6: 1.10, Infinite State Spaces Feb 7: Homework 4 due Feb 8: 5.1, Conditional Expectation Feb 10: 5.2, Martingale Examples
6 Feb 13: 5.3, Gambling Strategies Feb 14: Homework 5 due Feb 15: 5.4, Applications Feb 17: 2.1, Exponential Distribution
7 Feb 20: No class Feb 21: Homework 6 due Feb 22: 2.2 Poisson Process Feb 24: 2.2, Poisson Process
8 Feb 27: Midterm #2 Feb 28: No homework due Mar 1: 2.2, Poisson Process Mar 3: 2.3, Compound Poisson Process
9 Mar 6: 2.4, Transformations Mar 7: Homework 7 due Mar 8: 2.4, Transformations Mar 10: 3.1, Laws of Large Numbers
10 Mar 13: 3.2, Queueing Theory Mar 14: Homework 8 due Mar 15: 6.6, Brownian Motion Mar 17: Review of course

Advice on succeeding in a math class:

Homework Exam Solutions Supplementary Notes