Details of MA4203 (Spring 2025)
| Level: 4 | Type: Theory | Credits: 4.0 |
| Course Code | Course Name | Instructor(s) |
|---|---|---|
| MA4203 | Probability II | Anirvan Chakraborty |
| Syllabus |
|---|
| Quick review of concepts and results (without proof) from basic discrete and continuous random variables, 1-1 correspondence between distribution functions and probabilities on $\mathbbR$, examples of probability measures in Euclidean space, a metric on the space of probability measures on $\mathbbR^d$, expectation and the convergence theorems, independence, Borel-Cantelli lemma, weak and strong laws in the $iid$ cases, Kolmogorov's 0-1 law and three-series theorem, various modes of convergence, infinite products, Kolmogorov's consistency theorem, characteristic functions, uniqueness, inversion theorem, Levy continuity theorem, proof of CLT for the $iid$ case with finite variance, martingales, infinitely divisible laws and stable laws. |
| Prerequisite |
|---|
| Analysis IV (MA3204) and Topology (MA3201). |
| References |
|---|
| Suggested Texts:
1)Athreya, K.B. and Lahiri, S.N., Measure Theory and Probability Theory, Springer. 2)Ash, R. and Dolans-Dade, C.A., Probability and Measure Theory, Academic Press 3)Billingsley, P., Probability and Measure, John Wiley. 4)Borkar, V.S., Probability Theory : An Advanced Course, Springer. 5)Chung, K.L., A Course in Probability Theory, Elsevier. 6)Durrett, R., Probability : Theory and Examples, Cambridge University Press. 7)Gut, A., Probability : A Graduate Course, Springer. 8)Lo\`eve, M., Probability Theory, Vols. I \& II, Springer. 9)Parthasarathy, K.R., Introduction to Probability and Measure, Hindustan Book Agency. |
Course Credit Options
| Sl. No. | Programme | Semester No | Course Choice |
|---|---|---|---|
| 1 | IP | 2 | Not Allowed |
| 2 | IP | 4 | Not Allowed |
| 3 | IP | 6 | Not Allowed |
| 4 | MP | 2 | Not Allowed |
| 5 | MP ( Mathematical Sciences ) | 4 | Core |
| 6 | MR | 2 | Not Allowed |
| 7 | MR | 4 | Not Allowed |
| 8 | MS | 10 | Elective |
| 9 | MS | 4 | Not Allowed |
| 10 | MS | 6 | Not Allowed |
| 11 | MS ( Mathematical Sciences ) | 8 | Core |
| 12 | RS | 1 | Elective |
| 13 | RS | 2 | Elective |