Stat-570. Syllabus.

1. Conditional expectations. Ch.3, Sec.6.1-2; Ch.6, Sec.5.1-2.

2. Markov chains. Ch.5, Sec.1, 2, 3, 5; Ch.4, Sec.1,3.

3. Stochastic processes in continuous time: Preliminaries. Ch.12.

4. Poisson process. Ch.13, Sec.1.

5. Birth and Death processes. Ch.13, Sec.2.

6. Martingales in discrete time. Ch.15, Sec.1,2.

7. Brownian motion and martingales in continuous time. Ch.16, Sec.1,2.

8. More on dependency structures. Ch.17, Sec.1.