Text: Introduction to Stochastic Processes, 2nd Edition, by Gregory Lawler
| Date |
Topic |
Assigned Work and Links |
Due Date |
| 1/25-1/29 | |||
| M |
Introduction to stochastic processes and R To install: R and RStudio To use via server: r.amherst.edu |
Read Chapter 0 Intro to R |
|
| W |
1.1 Finite Markov chains | R script for Section 1.1 demos | |
| Th | 1.2 Large-time behavior | R script for Section 1.2 demos | |
| F |
1.2, cont'd | Article with proof of theorem (using right eigenvectors) | |
| 2/1-5 |
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| M |
Markov chain diffusion | Markov chain diffusion (R markdown file) | Due Fri 2/5 |
| W |
1.3 Classification of states | R script for Section 1.3 demos | |
| Th |
1.4 Return times | R script for Section 1.4 demos | |
| F |
1.5 Transient states | Exercises 1.9, 1.13, 1.14, 1.15 R script for Section 1.5 demo |
Due Fri 2/12 |
| 2/8-12 |
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| M |
Walk on a Graph | Walk on a Graph (R markdown file, graph) | Due Mon 2/15 |
| W |
1.6 Examples | R script for Section 1.6 demo | |
| Th |
2.1 Countable Markov chains | ||
| F |
2.2 Recurrence and transience | ||
| 2/15-2/19 | |||
| M |
Walk on a Circle | Due Mon 2/22 | |
| W |
2.3 Positive recurrence and null recurrence | ||
| Th |
Continue 2.3 | Exercises 2.3, 2.4, 2.8ab, 2.9 | Due Thurs 2/25 |
| F |
2.4 Branching processes | Branching Process Demo | |
| 2/22-2/26 |
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| M |
Branching processes | Branching processes (R markdown file) | Due Fri 2/26 |
| W |
Finish Chapter 2 | ||
| Th |
Review | Take-home exam (R markdown file) | Due Mon 2/29 |
| F |
3.1 Poisson processes | Poisson Process Demo | |
| 2/29-3/4 |
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| M | Poisson Processes | Rmarkdown file and data file | Due Fri 3/4 |
| W |
3.1 cont'd | R script for Section 3.2 demo | |
| Th |
3.2 Finite space space | ||
| F |
3.2 cont'd | Exercises 3.5, 3.9. 3.11 | Due Fri 3/11 |
| 3/7-3/11 |
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| M |
Coupon Collector | Coupon collector (R markdown file) | Due Fri 3/11 |
| W |
3.3 Birth-and-death processes | ||
| Th |
3.4 General case | ||
| F |
4.1 Optimal stopping | R script for Section 4.1 demo Exercise 4.1: compute numerically using un and also geometrically using convex hull |
|
| 3/12-3/20 |
Spring Recess | ||
| 3/21-3/25 | |||
| M |
Queueing | Queueing (R markdown file) | Due Fri 3/25 |
| W |
Finish stopping time | ||
| Th |
5.1 Martingales | ||
| F |
5.2 Definition and examples | 5.2 (replacing X₂ with X₃), 5.5, 5.7 | Due Fri 4/1 |
| 3/28-4/1 |
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| M |
Polya Urn | Polya Urn (R markdown file) | Due Fri 4/1 |
| W |
Continue martingales | ||
| Th |
5.3 Optional sampling theorem | Take-home exam (R markdown file) | Due Wed 4/6 |
| F |
7.1 Reversible processes | Poisson process demo and Mathematica demo | |
| 4/4-4/8 |
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| M |
7.2 Convergence to equilibrium | ||
| W |
Rejection Sampling | Rejection Sampling (R markdown file) | Due Fri 4/8 |
| Th |
7.3 Markov chain algorithms: Metropolis-Hastings algorithm |
7.1, 7.9, 7.10 | Due Fri 4/15 |
| F |
Gibbs sampler | Project topic due today (email by 4pm) |
|
| 4/11-4/15 |
|||
| M |
Decryption using MCMC | Decryption (R markdown file) AustenCount input file Encrypted message Helper R script |
Due Fri 4/15 |
| W |
7.4 Criterion for recurrence | ||
| Th |
8.1 Brownian motion | ||
| F |
8.2 Markov property | 8.4, 8.7, 8.10, 8.15 (integration demo) | Due Fri 4/29 |
| 4/18-4/22 |
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| M |
Brownian Motion | Brownian Motion (R markdown file) | Due Fri 4/22 |
| W |
Continue Brownian motion | ||
| Th |
8.3 Zero set of Brownian motion | Zero set demo | |
| F |
8.4 Brownian motion in several dim. |
PDE examples (Mathematica file from class) Outline of project due today (email by 4pm) |
|
| 4/25-4/29 |
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| M |
More Brownian Motion 8.5 Recurrence and transience |
More Brownian Motion (R markdown file) | Due Fri 4/29 |
| W |
9.1 Integration wrt random walk | ||
| Th |
9.2 Integration wrt brownian motion Presentations |
||
| F |
9.3 Ito's formula Presentations |
||
| 5/2-5/6 |
|||
| M |
Finish stochastic integration Presentations |
Project reports due today (email by 4pm) | |
| W |
Presentations | (final exam posted today) | |
| Th |
Presentations | ||
| F | Presentations | ||
| Take-home final exam due 4pm Thurs 5/12 |
