MATH180B Introduction to Stochastic Processes I, Winter 2019

Instructor: Tianyi Zheng (tzheng2@math.ucsd.edu) 
Lectures:   3:00-3:50PM on MWF in Center Hall 105

Section B01 (8:00-8:50 AM on Tuesdays in AP&M 2402), TA: Fangchen Li (fal025@ucsd.edu)

Section B02 (9:00-9:50 AM on Tuesdays in AP&M 2402), TA: Yesheng Huang (yeh018@ucsd.edu)

Section B03 (10:00-10:50 AM on Tuesdays in WLH 2208), TA: Yesheng Huang (yeh018@ucsd.edu)

Section B04 (11:00-11:50 AM on Tuesdays in WLH 2208), TA: Zonglin Han (zoh003@ucsd.edu)

Office Hours

Tianyi Zheng: 4PM-5:30PM on Mondays and Wednesdays in AP&M 6202

Fangchen Li: 3:30PM-4:30PM on Thursdays and 8PM-9PM on Thursdays in AP&M 5218

Yesheng Huang: 5PM-7PM on Mondays and 2PM-4PM on Thursdays in AP&M 6452

Zonglin Han: 1PM-3PM on Thursdays in AP&M 6436

Textbook

Although not mandatory, it is highly recommended to have the following two textbooks to consult besides lecture notes.

_ An Introduction to Stochastic Modeling by Mark Pinsky and Samuel Karlin.

_ Essentials of Stochastic Processes by Rick Durrett (which is written at a slightly more advanced level but is available online through the UCSD library web site).

Homework Assignments

Regular homework assignments will be posted in TritonEd. 

For those of you on the waiting list, class notes and homework assignment for the first week are here:

Week 1 Monday notes. Week 1 Wednesday notes. Week 1 Friday notes.

Homework1.

You will submit your Math 180B homework papers using a program called Gradescope. Your login name is your UCSD email address. Upon logging in, you should see an icon for Math 180B. Click on this icon, and then click on the name of the assignment that you want to submit. Then follow the instructions to submit the assignment. You can either submit assignments as a single PDF file, in which case you will have to tell Gradescope on which page one can find the answer to each question, or as a picture for each question. Click here for a video demonstrating the submission process, provided by Gradescope. 

You have several options for creating the PDF file to submit to Gradescope:

_ You could type your homework solutions in LaTeX and upload the PDF file. Learning LaTeX is certainly not required for the course, but it may be beneficial if you expect to pursue a career that will involve scientific writing. Click here for a LaTeX file that is designed to help you learn how to type homework solutions in LaTeX.

_ You could write your homework by hand and produce a PDF using one of the scanners on campus. Click here for instructions on where to find scanners on campus.

_ You could write your homework by hand and scan it using an iOS phone or Android phone. Click here for instructions.

_ You could submit photos of your homework instead of a PDF file. However, if you do this, please make sure that your photo can be read easily by the grader.

Exams

There will be two midterm exams and a final exam. The midterm exams will be held in class on Wednesday January 30, and Wednesday February 27. The final exam will be at 3PM-6PM on Wednesday March 20. Please bring your student ID to the exams.

You will be allowed to use one $8.5 by 11 inches page of notes on exams, and you may write 2 on both sides of the page. Grading Homework will count for 20 percent of the final grade. The lowest homework score will be dropped. Each midterm will count for 20 percent, and the final exam will count for 40 percent; alternatively, you may drop one lower midterm and the final exam will count for 60 percent. Syllabus and Course Schedule Here is a link to the syllabus. Here is the course schedule (not finalized, will be updated). KP stands for the textbook by Karlin-Pinsky textbook, D stands for the textbook by Durrett. Week Topic Sections in textbooks 1 Conditional distributions: discrete case [KP: 2.1] Conditional distributions: continuous case [KP: 2.4] Conditional expectation [KP: 2.3] 2 Covariance and correlation, variance of sums Multivariate normal distribution (two lectures) 3 Introduction to Markov chains [KP:3.1,3.3] Transition matrices [KP:3.2] [D:1.2] 4 First step analysis [KP:3.4] First Midterm Hitting probabilities [KP:3.4,3.5] [D: 1.9] 5 Mean hitting probabilities [KP:3.4,3.5] [D: 1.10] More examples of Markov chains [KP:3.5,3.6] 6 Recurrence and transience (two lectures) [KP:4.3] [D: 1.3] Stationary distribution [KP:4.1,4.2] [D: 1.4-1.5] 7 Stationary distributions (continued) [KP:4.1,4.2] [D: 1.4-1.5] Long run behavior of Markov chains [KP:4.4] [D: 1.6-1.8] 8 Long run behavior of Markov chains (continued) [KP:4.4] [D: 1.6-1.8] Second midterm Branching processes [KP:3.8,3.9] [D: 1.11] 9 Poisson processes: definition and basic properties [KP:5.1,5.2] [D: 2.2] Poisson processes: times between events (two lectures) [KP:5.3,5.4] [D: 2.2] 10 Superposition and thinning of Poisson processes [D: 2.2.2] Inhomogeneous and spatial Poisson processes [KP: 5.5] [D: 2.3] Review Session $