STAT545: Applied Stochastic Processes

Winter 2026

Logistics & course at a glance

About the course:

Graduate-level intro to Markov processes in discrete and continuous time, MCMC applications, and a brief look at Brownian motion and Gaussian processes.

Course site: https://ruizt.quarto.pub/stat545

Instructor: Trevor Ruiz (he/him) truiz01@calpoly.edu

Office hours: MW 1:00–2:30pm (25-236) or by appointment https://calendly.com/tdruiz/office-hour

Topics

Texbook: Dobrow, Introduction to Stochastic Processes with R.

Subjects covered:

  • discrete-time Markov chains (weeks 1-4, ch. 2-3)
  • Markov Chain Monte Carlo (MCMC) (weeks 5-6, ch. 5)
  • continuous-time Markov processes (weeks 7-9, ch. 6-7)
  • Brownian motion and Gaussian processes (week 10, ch. 8)

Mixture of application, computation/simulation, and theory.

Assessments and grades

  • Homeworks: 20%
  • Mini-projects: 30%
  • Participation: 10%
  • Midterm: 20%
  • Final: 20%

Tentative ranges: A (90,100], B (80,90], C (65,80], D (50,65], F [0,50]. Final distribution will be announced at end of quarter.

See syllabus for details.

Mini-projects & participation

Mini-projects

  • 2 projects in pairs; 15m presentation + 2p written summary
  • Everyone does discrete models + choose MCMC or continuous models

Participation

  • Volunteer at least once to present a textbook example
  • 7/10 for meeting expectation; remainder based on overall quality

Late work (homeworks)

  • Personal exceptions (anytime):
    • 1 HW up to 1 week late (no penalty)
    • 1 HW may be missed (no penalty)
  • After exceptions: HW ≤1 week late = 50% credit; later = 0
  • If no HW missed, lowest HW score dropped
  • No other late work unless an exception is granted

AI use

AI is OK for secondary tasks, not OK for primary tasks

  • Secondary tasks: explain concepts, look up definitions, generate examples, explain problem-solving strategies, etc.
  • Primary tasks: solving problems or completing assignments
  • Avoid pasting homework/exam prompts into AI tools
  • Prefer Cal Poly ChatGPT Edu for privacy

See link in syllabus to CSU AI Commons for guidance on ethical use.