STAT 253/317: Schedule

Cong Ma, University of Chicago, Winter 2026

Week Date Lec Topic Reading Homework
1 Tue Jan 6 1 Course overview; Definition, Transition Matrix, Core Examples RD Chapters 1 and 2
1 Thu Jan 8 2 n-Step Transition Probabilities, Limiting Distributions and Stationarity RD Chapters 2 and 3
2 Tue Jan 13 3 Irreducibility, Periodicity, Recurrence, Transience RD Chapter 3 HW 1 due
2 Thu Jan 15 4 Positive recurrence, ergodicity, and limit theorems RD Chapter 3
3 Tue Jan 20 5 Limit theorems, reversibility RD Chapter 3 HW 2 due
3 Thu Jan 22 6 Gambler's ruin problem and the first-step analysis
4 Tue Jan 27 7 Branching processes and generating functions HW 3 due
4 Thu Jan 29 8 Introduction to martingales: definition and basic examples
5 Tue Feb 3 9 Midterm exam HW 4 due on Feb 1
5 Thu Feb 5 10 Poisson process: definition, stationary and independent increments
6 Tue Feb 10 11 Poisson process: interarrival times, thinning, superposition
6 Thu Feb 12 12 Continuous-time Markov chains: definition, exponential holding times HW 5 due on Feb 15
7 Tue Feb 17 13 CTMCs: jump chains and generator (Q-matrix)
7 Thu Feb 19 14 Kolmogorov forward and backward equations
8 Tue Feb 24 15 Birth–death processes and stationary distributions HW 6 due on Feb 24
8 Thu Feb 26 16 Brownian motion: definition and basic properties
9 Tue Mar 3 17 Brownian motion: martingales and hitting times
9 Thu Mar 5 18 Brownian motion: reflection principle and first-passage probabilities