**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)ucla.edu

**Office Hours:** Fridays, 830AM-1030AM, MS
5634

**Lecture Meeting Time/Location:** Monday, Wednesday and Friday,
11AM-1150AM, MS 5117

**TA:**Yuming Zhang, yzhangpaul(@-symbol)math.ucla.edu

**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:**

- 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.

- 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 Tuesday and turned
in at the
**beginning**of the discussion section on the following Tuesday. - 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.

- 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 |

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:**

- 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.