PSTAT 160A Applied Stochastic Processes Spring 2020

(This version: 3/30/20)

Instructor: Zhijian Li ([email protected])

Lectures: Tuesday & Thursday 11:00 p.m. – 12:15 p.m. in Zoom

https://ucsb.zoom.us/j/498424882?pwd=bmdnSG5wbGFibDBqei9yK2pSZnRGdz09

Password: 160160

Office Hours: Tuesday 10:00 a.m. – 10:55 a.m., Thursday 7:00 p.m. – 8:00 p.m. in Zoom

https://ucsb.zoom.us/j/697117750

Password: 160160

Course Webpage: See GauchoSpace and Piazza.

Teaching Assistants and Discussion Sections: See GauchoSpace and Piazza.

Prerequisites: Mathematics 4A or 4AI or 5A, Mathematics 8, and PSTAT 120A. A minimum letter

grade of C or better must be earned in each course.

Catalog Description: Discrete probability models. Review of discrete and continuous probability.

Conditional expectations. Simulation techniques for random variables. Discrete time stochastic

processes: random walks and Markov chains with applications to Monte Carlo simulation.

Textbooks:

1.) Robert P. Dobrow, Introduction to Stochastic Processes with R, John Wiley & Sons Inc.,

2016. (main reference)

2.) David F. Anderson, Timo Seppa¨la¨inen, Benedek Valko´, Introduction to Probability,

Cambridge University Press, 2018. (for review PSTAT 120A)

3.) David Stirzaker, Elementary Probability, 2nd edition, Cambridge University Press, 2003.

(Chapter 5.6 on Random Walk)

We will cover following topics (cf. also schedule below):

Chapter 1. Review of Discrete and Continuous Probability.

Chapter 2. Conditional Expectation.

Chapter 3. Moment Generating Functions.

Chapter 4. Tail Bounds & Limit Theorems.

Chapter 5. Random Walk.

Chapter 6. Markov Chains.

Chapter 7. Simulation and Markov Chain Monte Carlo.

Homework: There will be 7 Homework assignments. Homework problems will be posted every

Friday (starting from April 3rd) on Gauchospace and will be submitted on Gauchospace on

Tuesday before the lecture (due 11 a.m.) two weeks later. No late homework submission

will be accepted! Two problems will be graded by your TA. Graded homework will be discussed

during the sections. Homework will count for final grade (see below). The lowest homework grade

will be dropped.

Python Homework: There will be 6 Python Homework assignments. Python problem sheets in the

format of Jupyter Notebooks will be posted every Friday (starting from April 3rd) on Gauchospace

and will be due on Friday two weeks later at 11:59 p.m. They will be submitted via GauchoSpace.

Please submit your pdf file and your jupyter notebook file (.ipynb) with all coding and

results. Please give yourself enough time to submit your work. No late homework

submission will be accepted! Python homework will count for final grade (see below). The

lowest Python homework grade will be dropped.

Group Work Policy: You are strongly encouraged to discuss the homework problems and Python

programming problems together with your classmates on Piazza but you have to submit your own

work! Exact copies will all be graded with 0 points!

Exams:

Midterm Exam: Thursday, May 7, during normal lecture hours. You will download the midterm

on Gauchospace and then submit it on Gauchospace.

Final Exam: A complicated and difficult Take home final. More details will be given at

the end of this quarter.

You may need to open your camera during the midterm. One sided handwritten note may be allowed

in the midterm. Students will not be allowed to take makeup exams.

Grading: Your cumulative average will be based on whichever of the following two weighted averages

is better.

Scheme 1 Weight

Python Homework 15%

Homework 15%

Midterm 30%

Final Exam 40%

Scheme 2 Weight

Python Homework 15%

Homework 15%

Final Exam 70%

Your course grade will be determined by your cumulative average at the end of the term and will be

based on the following scale:

Release Monday, 6/8/2020 12PM. Submit by 6/10/2020 11:59 PM

Grade Percentage in Course

A 100− 93.00

A− 92.99− 90.00

B+ 89.99− 87.00

B 86.99− 83.00

B− 82.99− 80.00

C+ 79.99− 77.00

C 76.99− 73.00

C− 72.99− 70.00

D+ 69.99− 67.00

D 66.99− 63.00

D− 62.99− 60.00

F 59.99− 0

Academic Dishonesty: Academic dishonesty is considered a serious offense at UCSB. Students

caught cheating shall be subject to the sanctions and other remedies described in UCSB’s Academic

Misconduct Policy and Procedures. It is in your best interest to maintain your academic integrity!