- June 6, 2020

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!