Text: Introduction to Stochastic Processes with R by R. Dobrow (textbook R scripts and errata)
(freely available as Ebook through Five Colleges library catalog and through Moodle course page)
| Date |
Topic |
Assigned Work and Class Materials |
| 1/22-1/26 | ||
| M |
1.1-1.3 Introduction to stochastic processes and R To install: R and RStudio To use via server: r.amherst.edu |
Appendix A: 3.1, 3.2, 4.1, 4.4, 8.2, 9.1, 9.2 (due Mon 1/29) |
| W |
1.4 Review of conditional probability | R script for Chapter 1 demos |
| Th | 1.5 Review of conditional expectation | |
| F |
2.1-2 Markov chains | R script for Section 2.1 demos |
| 1/29-2/2 |
||
| M |
2.3 MC computations |
Exercises 2.2, 2.4, 2.5, 2.16, 2.27 (due Mon 2/5) |
| W |
2.4 Long-term behavior | R script for Section 2.4 demos |
| Th |
Markov chain diffusion (due Wed 2/7) | |
| F |
3.1-3.2 Limiting and stationary distributions | R script for Section 3.1 demos |
| 2/5-9 |
||
| M |
3.3 The way to state a | Exercises 3.3, 3.5, 3.10, 3.14, 3.27, 3.29 (due Mon 2/12) |
| W |
3.3, cont'd | |
| Th |
3.4 Irreducible Markov chains | R script for Section 3.4 demos |
| F |
3.5 Periodicity | R script for Section 3.5 demos |
| 2/12-2/16 | ||
| M |
3.6-7 Ergodic/Reversibility | Exercises 3.37, 3.46, 3.47, 3.59, 3.68 (due Mon 2/19) |
| W |
3.8 Absorbing chains | R script for Section 3.8 demos R script for Section 3.8 examples |
| Th |
Walk on a Graph and graph (due Mon 2/19) | |
| F |
Walk on a Circle (due Wed 2/21) | |
| 2/19-2/23 |
||
| M |
Review | Take-home exam 1 (due Mon 2/26) |
| W |
4.1-2 Branching processes intro | R script for Section 4.2 demos |
| Th |
4.3 Prob generating functions | R script for Section 4.3 demos Mathematics demo for prob gen fn |
| F |
4.4 Extinction | R script for Section 4.4 demos |
| 2/26-3/2 |
||
| M | Branching processes (due Fri 3/2) | Exercises 4.12, 4.14, 4.15, 4.17, 4.31 (due Mon 3/5) |
| W |
5.1 Markov chain Monte Carlo intro | R script for Section 5.1 demos |
| Th |
5.2 Metropolis-Hastings | |
| F |
Rejection Sampling (due Wed 3/7) | |
| 3/5-3/9 |
||
| M |
Decryption (due Fri 3/9) AustenCount input file Encrypted message Helper R script |
Exercises 5.1, 5.5 (due Mon 3/19) |
| W |
5.3 Gibbs sampler | |
| Th |
6.1 Poisson processes intro | |
| F |
6.2 Arrival and interarrival times | R script for Section 6.2 demos |
| 3/10-3/18 |
Spring Recess | |
| 3/19-3/23 | ||
| M |
Poisson processes and data file (due Fri 3/23) | Exercises 6.1, 6.3, 6.6, 6.7, 6.8, 6.15 (due Mon 3/26) |
| W |
6.3 Infinitesimal probabilities | |
| Th |
Finish chapter 6 | |
| F |
Coupon collector (due Mon 3/26) | |
| 3/26-30 |
||
| M |
Review | Take-home exam 2 (due Mon 4/2) |
| W |
7.1-2 Continuous-time MC intro | |
| Th |
7.3 Infinitesimal generator | R script for Section 7.3 demos |
| F |
7.4 Long-term behavior | R script for Section 7.4 demos |
| 4/2-4/6 |
||
| M |
7.5 Time reversibility | Exercises 7.2, 7.4, 7.6, 7.21, 7.23, 7.33 (due Mon 4/9) Mathematica demo |
| W |
7.6 Queueing theory | Project topic due today |
| Th |
Queueing (due Wed 4/11) | |
| F |
8.1 Brownian motion intro | R script for Section 8.1 demos |
| 4/9-4/13 |
||
| M |
8.2 Random walk |
(No assigned exercises--work on project) R script for Section 8.2 demos |
| W |
Brownian Motion (due Fri 4/13) | |
| Th |
8.4 Transformations and properties | Outline of project due today |
| F |
8.5 Variations and applications | R script for Section 8.4 demo |
| 4/16-4/20 |
||
| M |
8.6 Martingales | Exercises 8.2, 8.4, 8.5(b), 8.11, 8.23, 8.31 (due Mon 4/23) |
| W |
Polya's Urn (due Fri 4/20) | |
| Th |
9.1 Stochastic calculus intro 9.2 Ito integral |
|
| F |
No class |
|
| 4/23-4/27 |
||
| M |
Presentations |
(No assigned exercises--work on project) |
| W |
Presentations | |
| Th |
Presentations |
|
| F |
Presentations | |
| Take-home third exam due 4pm Thurs May 10 | Project reports due 4pm Tues May 8 |
