About the course

Instructor: Ethan Levien

Prerequisites: Knowledge of probability theory (20 or 60), Linear algebra (22 or 24) and Differential equations (23) will be assumed.

Course objectives: This is a course in stochastic processes designed to prepare graduate students in applied mathematics and related fields for research. The course will strike a balance between rigor and practical tools for solving applied problems. Specific topics include discrete and continuous time Markov chains (ergodic theory, Gillespie algorithms), Wiener process, Stochastic integration, Ito's Lemma, Fokker-Planck Equation, Spectral Theory. See weekly schedule for details.

My availability: I will hold office hours in person Monday 8:00am-10:00am or by appointment. I will be in my office most days 8-4:30, except Wednesday, when I work from home in the morning.

Course policies

Expectations: As this is a graduate course, I will expect a higher level of independence than an undergraduate course when it comes to navigating the material. Specifically, I will expect some familiarity with the definitions and notation in the assigned readings so that I can focus on providing additional context and examples, rather than explaining the basic concepts. No electronics are permitted during lectures.

Grades: The breakdown of your grade is as follows:

• Attendance (including quizzes) (20%)
• Midterm (20%)
• Final (40%)
• Projects (20%)
Exams are closed book.

Generative AI policy Use it, but not too much.

Textbooks:

• Primary text: Applied stochastic processes by Weinan E, Tiejun Li and Eric Vanden-Eijnden. Unless otherwise noted, all reading are from this book.
• References for some details on Markov chains and probability theory: Probability: Theory and Examples by Rick Durrett (RD)
• References for some proofs when we get to SDEs: An introduction to Stochastic Differential Equations by Lawrence C. Evans. (LE)

PDFs of all these texts can be obtained from the library.

Accessibility Needs

Students with disabilities who may need disability-related academic adjustments and services for this course are encouraged to see me privately as early in the term as possible. Students requiring disability-related academic adjustments and services must consult the Student Accessibility Services office (Carson Hall, Suite 125, 646-9900). Once SAS has authorized services, students must show the originally signed SAS Services and Consent Form and/or a letter on SAS letterhead to me. As a first step, if students have questions about whether they qualify to receive academic adjustments and services, they should contact the SAS office. All inquiries and discussions will remain confidential.