Stochastic Processes, Fall 2016

Course: MATH 171, Stochastic Processes, Fall 2016
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: 15 October 2016

Instructor: Steven Heilman, heilman(@-symbol)ucla.edu
Office Hours: Fridays, 10AM-12PM, MS 5634
Lecture Meeting Time/Location: Monday, Wednesday and Friday, 9AM-950AM, MS 5147
TA: Fangbo Zhang, fb.zhangsjtu(@-symbol)gmail.com
TA Office Hours: Tuesdays 2PM-3PM, MS 6153
Discussion Session Meeting Time/Location: Thursdays, 9AM-950AM, TBD
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, October 21, 9AM-950AM, PAB 1434A
Second Midterm: Monday, November 14, 9AM-950AM, Public Affairs 2270
Final Exam: Thursday, December 8, 8AM-11AM, Boelter 5440
Other Resources: An introduction to mathematical arguments, Michael Hutchings, An Introduction to Proofs, How to Write Mathematical Arguments
Email Policy:

My email address for this course is heilman(@-symbol)ucla.edu
It is your responsibility to make sure you are receiving emails from heilman(@-symbol)ucla.edu , and they are not being sent to your spam folder.
Do NOT email me with questions that can be answered from the syllabus.

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 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:

Late homework is not accepted.
If you still want to turn in late homework, then the number of minutes late, divided by ten, will be deducted from the score. (The time estimate is not guaranteed to be accurate.)
The lowest two homework scores will be dropped. This policy is meant to account for illnesses, emergencies, etc.
Do not submit homework via email.
There will be 8 homework assignments, assigned weekly on Thursday and turned in at the beginning of the discussion section on the following Thursday.
A random subset of the homework problems will be graded each week. However, it is strongly recommended that you try to complete the entire homework assignment.
You may use whatever resources you want to do the homework, including computers, textbooks, friends, the TA, etc. However, I would discourage any over-reliance on search technology such as Google, since its overuse could degrade your learning experience. By the end of the quarter, you should be able to do the entire homework on your own, without any external help..
All homework assignments must be written by you, i.e. you cannot copy someone else's solution verbatim.
Homework solutions will be posted on Friday after the homework is turned in.

Grading Policy:

The final grade is weighted as the larger of the following two schemes. Scheme 1: homework (15%), the first midterm (20%), the second midterm (25%), and the final (40%). Scheme 2: homework (15%), largest midterm grade (35%), final (50%). The grade for the semester will be curved. However, anyone who exceeds my expectations in the class by showing A-level performance on the exams and homeworks will receive an A for the class.
We will use the MyUCLA gradebook.
If you cannot attend one of the exams, you must notify me within the first two weeks of the start of the quarter. Later requests for rescheduling will most likely be denied.
You must attend the final exam to pass the course.

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

Week	Monday	Tuesday	Wednesday	Thursday	Friday
0				Sep 22: First discussion section. No homework due	Sep 23: A.1, A.2, Review of Probability
1	Sep 26: A.3, Review; Law of Large Numbers		Sep 28: Central Limit Theorem	Sep 29: Homework 0 (ungraded)	Sep 30: 1.1, Markov Chains
2	Oct 3: 1.1, Examples of Markov Chains		Oct 5: 1.3, Classification of States	Oct 6: Homework 1 due	Oct 7: 1.4, Stationary Distributions
3	Oct 10: 1.5, Limiting Behavior		Oct 12: 1.7, Proofs of Limiting Behavior	Oct 13: Homework 2 due	Oct 14: 1.7, Proofs of Limiting Behavior
4	Oct 17: 1.10, Infinite State Spaces		Oct 19: 5.1, Conditional Expectation	Oct 20: No homework due	Oct 21: Midterm #1
5	Oct 24: 5.2, Martingale Examples		Oct 26: 5.3, Gambling Strategies	Oct 27: Homework 3 due	Oct 28: 5.4, Applications
6	Oct 31: 2.1, Exponential Distribution		Nov 2: 2.2, Poisson Process	Nov 3: Homework 4 due	Nov 4: 2.2, Poisson Process
7	Nov 7: 2.2, Poisson Process		Nov 9: 2.3, Compound Poisson Process	Nov 10: Homework 5 due	Nov 11: No class
8	Nov 14: Midterm #2		Nov 16: 2.4, Transformations	Nov 17: Homework 6 due	Nov 18: 2.4, Transformations
9	Nov 21: 3.1, Laws of Large Numbers		Nov 23: Homework 7 due. 3.2, Queueing Theory	Nov 24: No class	Nov 25: No class
10	Nov 28: 6.6, Brownian Motion		Nov 30: 6.6, Brownian Motion	Dec 1: Homework 8 due	Dec 2: Review of course

Advice on succeeding in a math class:

Review the relevant course material before you come to lecture. Consider reviewing course material a week or two before the semester starts.
When reading mathematics, use a pencil and paper to sketch the calculations that are performed by the author.
Come to class with questions, so you can get more out of the lecture. Also, finish your homework at least two days before it is due, to alleviate deadline stress.
Write a rough draft and a separate final draft for your homework. This procedure will help you catch mistakes. Also, consider typesetting your homework. Here is a template .tex file if you want to get started typesetting.
If you are having difficulty with the material or a particular homework problem, review Polya's Problem Solving Strategies, and come to office hours.

Homework

HW0 HW1 HW2 HW3 HW4 HW5 HW6 HW7 HW8 (Solutions posted on CCLE)

Exam Solutions

Exam 1 Exam 1 Solutions Exam 2 Exam 2 Solutions Final Final Solutions

Supplementary Notes

Math 171 Lecture Notes