Subsections
[Cr:4, Lc:3, Tt:1, Lb:0]
- Markov Chains: Classification of states, Chapman-Kolmogorov Equation, Strong Markov Property, Stationary distribution, Convergence to stationarity.
- Transient/Recurrent behaviour of random walks, Reflection principle.
- Martingales: Stopping time, Doob’s inequality, Convergence theorems.
- Markov Process: Infinitesimal generator and Markov Semigroup, Birth and Death process.
- Poisson Process: Mapping theorem, Existence theorem, Queues.
- Markov Chain Mixing, Random Walks on Graphs.
- Sheldon M. Ross, Stochastic Processes, Wiley, 1995, ISBN-13: 9780471120629.
- R. Durrett, Probability: Theory and Examples, 4th edition, Cambridge University Press, ISBN: 9780521765398.
- W. Feller, An Introduction to probability theory, vol. 1, 1968 (3rd edition, ISBN-13: 9780471257080) and vol. 2 (2nd edition, ISBN-13: 978-0471257097), Wiley.
- J. F. C. Kingman, Poisson Processes, Oxford Science Publications,
Clarendon Press, 1993, ISBN-13: 9780198536932.
