Applied Stochastic Processes
Stochastic processes describe phenomena in which dependence arises from evolution across time (or space). Formally, they are probability models defined by indexed collections of random variables, with dependence usually characterized through conditional distributions. This course is a graduate-level introduction to stochastic processes covering several standard probability models — Markov processes, point processes, and Gaussian processes — and their applications in statistics, including Markov Chain Monte Carlo (MCMC) and selected modeling applications drawn from various domains.
Instructor: Trevor Ruiz (he/him) [email]
Class meetings: TR 9:00am–10:20am in 52-0E33
Office hours: TR 2:30pm–4:00pm in 25-236
Final exam: Tuesday 12/15/26 10:00am-12:30pm
Find a tentative schedule for the term and detailed course policies in the [course syllabus]. Please note the syllabus is subject to change. Readings, assignments, and materials (notes, scripts, etc.) will be posted below on a rolling basis.
Week 1 (8/24)
Introduction to stochastic processes; Markov chain basics
- Reading: syllabus; 1.2, 1.4-1.5, 2.1-2.2
- Handout 1 [pdf]
- Homework 1 exercises 2.1, 2.9, 2.10, 2.16, 2.27 (copy of gamblersruin.R), and prove the Markov Property, due Thursday 9/3 in class
Week 2 (8/31)
Limiting and stationary distributions on finite state spaces
- Reading: 2.3; 3.1-3.2
- Handout 2 [pdf]
- Simulating long-run behavior [R script]
- Homework 2 exercises 3.5, 3.7, 3.8, 3.63 (copy of utilities.R), due Thursday 9/10 in class
Week 3 (9/7)
Communication classes and their properties
- Reading: 3.3, 3.5, 3.8
- Handout 3 [pdf]
- Homework 3 exercises 3.23 (limit only, skip the ergodic part), 3.28, 3.29, 3.54, 3.66
Week 4 (9/14)
Limit theorem and extension to infinite state spaces