Introduction to Stochastic Processes 1

(STATS217, Winter 2023)

• Instructor: Tselil Schramm
• Time: Tuesdays & Thursdays, 10:30–11:50 Pacific
• Location: Huang 18
• TAs: Isaac Gibbs and Nathan Tung
• Office hours:
  • Monday 10:30-12:30; Sequoia 105 (Nathan)
  • Tuesday 10:30-12:30; 50-52e (Nathan)
  • Tuesday 15:15-16:15; 50-52e (Isaac)
  • Wednesday 10:30-12:30; Econ 139 (Isaac)
  • Wednesday 16:15-17:15; Zoom (Isaac)
  • Thursday 13:30-15:00; Sequoia 132 (Tselil)

Resources: Our official course text is ``Essentials of Stochastic Processes'' by Rick Durrett, freely available here. You may also find the following additional resources useful.

• Modern Discrete Probability: An Essential Toolkit, polished lecture notes for a course taught by Sebastien Roch.
• Slides from the previous iteration of this course, taught by Vishesh Jain.
• Markov Chains and Mixing Times, by Levin and Peres.

Prerequisites:

• Probability Theory (STATS116, CS109, MATH151, or equivalent).
• Linear Algebra (MATH51, CS205, or equivalent).
• Calculus (MATH19/MATH20/MATH21 or equivalent).

Course Policies: A detailed overview of course policies (including grading and assignments) can be found in the course syllabus.

Course description

This course is an introduction to discrete stochastic processes. We will see how to model real-world stochastic processes as simple, structured random systems, and how doing so gives us the power to draw remarkably precise, controlled conclusions about the macroscopic behavior of these chaotic processes. Topics covered include discrete and continuous time Markov Chains, Martingales, Poisson Processes, and some topics in Statistical physics. This is a rigorous, theoretical, proof-based course, but we will not require knowledge of measure theory.

Lectures and Reading

Below is a preliminary schedule (subject to change), including the readings relevant to each lecture.