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STAT 253/317: Syllabus
Cong Ma, University of Chicago, Winter 2026
Schedule
| Week | Date | Lec | Topic | Reading | Homework |
| 1 | Tue Jan 6 | 1 | Course overview; Definition, Transition Matrix, Core Examples | Text Ch. 1 | |
| 1 | Thu Jan 8 | 2 | Path Probabilities and n-Step Transitions | Text Ch. 1 | |
| 2 | Tue Jan 13 | 3 | Limiting Distributions and Stationarity | Text Ch. 1 | HW 1 due |
| 2 | Thu Jan 15 | 4 | Irreducibility, Recurrence, Transience | Text Ch. 1–2 | |
| 3 | Tue Jan 20 | 5 | Periodicity, positive recurrence, ergodicity, and reversibility | Text Ch. 2 | HW 2 due |
| 3 | Thu Jan 22 | 6 | Gambler's ruin problem and the first-step analysis | Text Ch. 2 | |
| 4 | Tue Jan 27 | 7 | Branching processes and generating functions | Text Ch. 2 | HW 3 due |
| 4 | Thu Jan 29 | 8 | Introduction to martingales: definition and basic examples | Notes | |
| 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 | Text Ch. 4 | |
| 6 | Tue Feb 10 | 11 | Poisson process: interarrival times, thinning, superposition | Text Ch. 4 | |
| 6 | Thu Feb 12 | 12 | Continuous-time Markov chains: definition, exponential holding times | Text Ch. 6 | HW 5 due on Feb 15 |
| 7 | Tue Feb 17 | 13 | CTMCs: jump chains and generator (Q-matrix) | Text Ch. 6 | |
| 7 | Thu Feb 19 | 14 | Kolmogorov forward and backward equations | Text Ch. 6 | |
| 8 | Tue Feb 24 | 15 | Birth–death processes and stationary distributions | Text Ch. 6 | HW 6 due on Feb 24 |
| 8 | Thu Feb 26 | 16 | Brownian motion: definition and basic properties | Text Ch. 8 | |
| 9 | Tue Mar 3 | 17 | Brownian motion: martingales and hitting times | Text Ch. 8 | |
| 9 | Thu Mar 5 | 18 | Brownian motion: reflection principle and first-passage probabilities | Text Ch. 8 | |
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