Text: Introduction to Stochastic Processes, 2nd Edition, by Gregory Lawler
| Date |
Topic |
Assigned Work and Links |
Due Date |
| 1/23-1/24 | |||
| Th |
Introduction to stochastic processes and R (R and RStudio) |
Read Chapter 0 Intro to R |
|
| F |
1.1 Finite Markov chains | R script for Section 1.1 demos | |
| 1/27-1/31 |
|||
| M | 1.2 Large-time behavior | R script for Section 1.2 demos | |
| W |
1.2, cont'd | Article with proof of theorem (using right eigenvectors) | |
| Th |
Lab #1 | Tues 2/4 | |
| F |
1.3 Classification of states | R script for Section 1.3 demos | |
| 2/3-2/7 |
|||
| M |
1.4 Return times | R script for Section 1.4 demos | |
| W |
1.5 Transient states | Exercises 1.9, 1.13, 1.14, 1.15 R script for Section 1.5 demo |
Fri 2/7 |
| Th |
Lab #2 | Tues 2/11 | |
| F |
1.6 Examples | R script for Section 1.6 demo | |
| 2/10-2/14 |
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| M |
2.1 Countable Markov chains | ||
| W |
2.2 Recurrence and transience | ||
| Th |
Lab #3 | Wed 2/19 | |
| F |
2.3 Positive recurrence and null recurrence | ||
| 2/17-2/21 | |||
| M |
Continue 2.3 | Exercises 2.3, 2.4, 2.8ab, 2.9, 2.14 | Mon 2/24 |
| W |
2.4 Branching processes | Branching Process Demo | |
| Th |
Lab #4 | ||
| F |
Finish Chapter 4 | Tues 2/25 | |
| 2/24-2/28 |
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| M |
Review | Mon 3/3 | |
| W |
3.1 Poisson processes | Poisson Process Demo | |
| Th |
Lab #5 | Data file | Tues 3/4 |
| F |
More on Poisson processes | ||
| 3/3-3/7 |
|||
| M | 3.2 Finite space space | R script for Section 3.2 demo | |
| W |
3.2 cont'd | Exercises 3.5, 3.9. 3.11 | Mon 3/10 |
| Th |
Lab #6 | Tue 3/11 | |
| F |
3.3 Birth-and-death processes | ||
| 3/10-3/14 |
|||
| M |
3.4 General case | ||
| W |
4.1 Optimal stopping | R script for Section 4.1 demo | |
| Th |
Lab #7 | Wed 3/26 | |
| F |
Finish stopping time | Exercise 4.1: compute numerically using un and also geometrically using convex hull | Mon 3/24 |
| 3/15-3/23 |
Spring Recess | ||
| 3/24-3/29 | |||
| M |
5.1 Martingales | ||
| W |
5.2 Definition and examples | 5.2, 5.5, 5.7 | Wed 4/2 |
| Th |
Lab #8 | Wed 4/2 | |
| F |
Continue martingales | ||
| 3/31-4/4 |
|||
| M |
5.3 Optional sampling theorem | ||
| W |
7.1 Reversible processes | Wed 4/9 | |
| Th |
Lab #9 | Tues 4/8 | |
| F |
7.2 Convergence to equilibrium | ||
| 4/7-4/11 |
|||
| M |
7.3 Markov chain algorithms: Metropolis-Hastings algorithm |
||
| W |
Gibbs sampler | ||
| Th |
Lab #10 | Tues 4/15 | |
| F |
7.4 Criterion for recurrence | 7.1, 7.9, 7.10 | Wed 4/16 |
| 4/14-4/18 |
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| M |
8.1 Brownian motion | Project topic due today (email by 4pm) | |
| W |
8.2 Markov property | ||
| Th |
Lab #11 | ||
| F |
Continue Brownian motion | 8.4, 8.7, 8.10, 8.15 (integration demo) | Mon 4/28 |
| 4/21-4/25 |
|||
| M |
8.3 Zero set of brownian motion | Outline of project due today (email by 4pm) | |
| W |
8.4 Brownian motion in several dim. |
Examples (Mathematica file from class) | |
| Th |
Lab #12 | ||
| F |
8.5 Recurrence and transience |
||
| 4/28-5/2 |
|||
| M |
9.1 Integration wrt random walk | Project presentations begin | |
| W |
9.2 Integration wrt brownian motion | ||
| Th |
Presentations (in Webster 102) | ||
| F |
9.3 Ito's formula | ||
| 5/5-5/7 |
|||
| M |
More on stochastic integration | ||
| W |
Finish stochastic integration | Project reports due today (email by 4pm) | |
| Take-home final exam due 4pm Wed May 14 |