Details of MA3108 (Autumn 2022)
| Level: 3 | Type: Theory | Credits: 4.0 |
| Course Code | Course Name | Instructor(s) |
|---|---|---|
| MA3108 | Stochastic Processes and Its Applications | Anirvan Chakraborty |
| Syllabus |
|---|
| Quick review of probability theory: Probability spaces, random variables, probability
distributions, expectations, transforms and generating functions, convergence, LLNs, CLT. Introduction to stochastic processes: Definition and examples; classification of random processes. Discrete-time Markov chain: Definition and examples; homogeneous Markov chain; transition probability matrix, Chapman-Kolmogorov equations; limiting probabilities; ergodicity; stationary distribution; random walk; gamblers ruin problem; different applications of Markov chains including an introduction to MCMC techniques. Discrete-time Martingales: Definitions and examples; sub/super-martingales; stopping times; optional sampling theorem; martingale inequalities; reverse martingales; convergence theorems; applications. Continuous-time Markov chain: Definition and examples; Birth & death process; Poisson process; Holding times and transitions; Transition rate and transition probabilities; Kolmogorov forward and backward equations; infinitesimal generator and jump chain; classification of states; (if time permits) long-run behaviour of continuous-time Markov chains. |
| References |
|---|
| 1. Ross; Introduction to Probability Models, Academic Press.
2. Taylor and Karlin; An Introduction to Stochastic Modelling, Academic Press. 3. Ross; Stochastic Processes, Wiley India. 4. Karlin and Taylor; A First Course in Stochastic Processes, Academic Press. 5. Hoel, Port, and Stone; Introduction to Stochastic Processes, Waveland Press. 6. Resnick; Adventures in stochastic processes, Birkhauser. 7. Billingsley; Probability and Measure, Wiley. |
Course Credit Options
| Sl. No. | Programme | Semester No | Course Choice |
|---|---|---|---|
| 1 | IP | 1 | Not Allowed |
| 2 | IP | 3 | Not Allowed |
| 3 | IP | 5 | Not Allowed |
| 4 | MP | 1 | Core |
| 5 | MP | 3 | Not Allowed |
| 6 | MR | 1 | Not Allowed |
| 7 | MR | 3 | Not Allowed |
| 8 | MS | 3 | Not Allowed |
| 9 | MS | 5 | Not Allowed |
| 10 | MS | 7 | Not Allowed |
| 11 | MS | 9 | Not Allowed |
| 12 | RS | 1 | Not Allowed |
| 13 | RS | 2 | Not Allowed |