| Name | Role | Office | Zoom link | |
| Yuriy Nemish | Instructor | APM 6442 | ynemish@ucsd.edu | link |
| Lectures | Monday, Wednesday, Friday 4:00 - 4:50 PM |
| Office hours | Thursday 1:30 - 3:00 PM |
Welcome to Math 285: a one quarter course in stochastic processes. According to the UC San Diego Course Catalog, the topics covered are Markov chains, hidden Markov models, martingales, Brownian motion, Gaussian processes.
Here is a more detailed listing of course topics, in the sequence they will be covered, together with the relevant section(s) of the textbook. While each topic corresponds to approximately one lecture, there will be some give and take here. This is a rough schedule that will be updated during the term. (TBA)
| Lecture | Week | Topic | Lawler | Slides | Videos | Preliminary Slides |
|---|---|---|---|---|---|---|
| 1/3 | 1 | Introduction. Definition of Markov processes | § 1.1 | Slides 1 | Slides 1 | |
| 1/5 | 1 | Transition probabilities. Hitting times | - | Slides 2 | Slides 2 | |
| 1/7 | 1 | Hitting times. First step analysis | - | Slides 3 | Lecture 3 | Slides 3 |
| 1/10 | 2 | First step analysis. Stopping times | - | Slides 4 | Lecture 4 | Slides 4 |
| 1/12 | 2 | Irreducible Markov chains. Random walks of graphs | - | Slides 5 | Lecture 5 | Slides 5 |
| 1/14 | 2 | Stationary distributions. Long-run behaviour | § 1.2 | Slides 6 | Lecture 6 | Slides 6 |
| 1/19 | 3 | Periodic, aperiodic, reducible, irreducible Markov chains | § 1.3 | Slides 7 | Lecture 7 | Slides 7 |
| 1/21 | 3 | Markov chains with finite state space | §§ 1.3, 1.5 | Slides 8 | Lecture 8 | Slides 8 |
| 1/24 | 4 | Markov chains with infinite state space | §§ 1.3, 2.3 | Slides 9 | Lecture 9 | Slides 9 |
| 1/26 | 4 | Positive and null recurrence | §§ 2.3 | Slides 10 | Lecture 10 | Slides 10 |
| 1/28 | 4 | Positive and null recurrence | §§ - | Slides 11 | Lecture 11 | Slides 11 |
| 1/31 | 5 | Ergodic theorem | §§ - | Slides 12 | Lecture 12 | Slides 12 |
| 2/2 | 5 | Time reversal | §§ 7.1 | Slides 13 | Lecture 13 | Slides 13 |
| 2/4 | 5 | MCMC | §§ 7.3 | Slides 14 | Lecture 14 | Slides 14 |
| 2/7 | 6 | Branching processes | §§ 2.4 | Slides 15 | Lecture 15 | Slides 15 |
| 2/9 | 6 | Hidden Markov Models | §§ - | Slides 16 | Lecture 16 | Slides 16 |
| 2/11 | 6 | Hidden Markov Models. Viterbi algorithm | §§ - | Slides 17 | Lecture 17 | Slides 17 |
| 2/14 | 7 | Continuous-time Markov chains | §§ 3.1-3.2 | Slides 18 | Lecture 18 | Slides 18 |
| 2/16 | 7 | Strong Markov property. Embedded jump chain. Infinitesimal description | §§ 3.1-3.4 | Slides 19 | Lecture 19 | Slides 19 |
| 2/18 | 7 | Kolmogorov's equations. Poisson processes | §§ 3.1-3.4 | Slides 20 | Lecture 20 | Slides 20 |
| 2/23 | 8 | Poisson processes. Birth and death chains | §§ 3.1-3.4 | Slides 21 | Lecture 21 | Slides 21 |
| 2/25 | 8 | Recurrence and transience. Stationary distributions | §§ 3.1-3.4 | Slides 22 | Lecture 22 | Slides 22 |
| 2/28 | 9 | Long-run behavior of continuous-time MC. Conditional expectation | §§ 5.1 | Slides 23 | Lecture 23 | Slides 23 |
| 3/2 | 9 | Martingales | §§ 5.2-5.3 | Slides 24 | Lecture 24 | Slides 24 |
| 3/4 | 9 | Martingales. Doob's maximal inequality | §§ 5.6 | Slides 25 | Lecture 25 | Slides 25 |
| 3/7 | 10 | Martingale convergence theorem | §§ 5.5 | Slides 26 | Lecture 26 | Slides 26 |
Lecture: You are responsible for material presented in the lecture whether or not it is discussed in the textbook. You should expect homework questions that will test your understanding of concepts discussed in the lecture.
Homework: Homework assignments are posted below, and will be due at 11:59 PM on the indicated due date. You must turn in your homework through Gradescope; if you have produced it on paper, you can scan it or simply take clear photos of it to upload. Your lowest homework score will be dropped. It is allowed and even encouraged to discuss homework problems with your classmates and your instructor, but your final write up of your homework solutions must be your own work.
Evaluation: There will be no exams in this course. Your grade will be determined by your homework.
Administrative Links: Here are two links regarding UC San Diego policies on exams:
Regrade Policy:
Grading:
Your course grade will be based on the following scale:
| A+ | A | A- | B+ | B | B- | C+ | C | C- |
| 97 | 93 | 90 | 87 | 83 | 80 | 77 | 73 | 70 |
The above scale is guaranteed: for example, if your cumulative average is 80, your final grade will be at least B-. However, your instructor may adjust the above scale to be more generous.
Academic Integrity: UC San Diego code of academic integrity outlines the expected academic honesty of all studentd and faculty, and details the consequences for academic dishonesty. The main issues are cheating and plagiarism, of course, for which we have a zero-tolerance policy. (Penalties for these offenses always include assignment of a failing grade in the course, and usually involve an administrative penalty, such as suspension or expulsion, as well.) However, academic integrity also includes things like giving credit where credit is due (listing your collaborators on homework assignments, noting books or papers containing information you used in solutions, etc.), and treating your peers respectfully in class. In addition, here are a few of our expectations for etiquette in and out of class.
Weekly homework assignments are posted here. Homework is due by 11:59 PM on the posted date, through Gradescope. Late homework will not be accepted.