STA 447/2006: Stochastic Processes
Wenlong Mou, Department of Statistical Sciences, University of Toronto, Winter 2026
Schedule
| lecture | topic | book chapteres | notes |
| 01/07 | introduction, Markov definitions and transition probabilities, recurrent and transient states, recurrent state theorem, recurrence of (multi-dimensional) random walks | Rosenthal 1.1 – 1.5 | Lecture 1 |
| 01/14 | Proof of recurrence state theorem, f-expansion, relation between recurrence and transience of different states, equivalent characterization of recurrent/transient Markov chains | Rosenthal 1.6, 1.7 | Lecture 2 |
| 01/21 | Recurrence equivalence continued, reducible Markov chains, stationary distributions and stationary measures, detailed balance condition, vanishing transition probabilities and non-existence results, periodicity | Rosenthal 1.6, 2.1 – 2.3, Lawler 1.3 | Lecture 3 |
| 01/28 | | | |
| 02/04 | Midterm exam #1 | | |
| 02/11 | | | |
| 02/25 | | | |
| 03/04 | | | |
| 03/11 | Midterm exam #2 | | |
| 03/18 | | | |
| 03/25 | | | |
| 04/02 | | | |
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Recommended practice questions
Week 1: Rosenthal 1.3.9, 1.4.8, 1.5.4, 1.5.9
Week 2: Rosenthal 1.5.13, 1.5.14, 1.6.20, 1.6.21, 1.6.25, 1.7.12
Week 3: Rosenthal 2.1.3, 2.4.13, 2.4.14, 2.4.15, 2.4.16, Lawler 1.7, Durrett 1.70, 1.72
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