Review of Basic undergraduate probability: Random variables, Standard discrete and continuous distributions, Expectation, Variance, Conditional Probability.
Discrete time Markov chains: countable state space, classification of states
Characteristic functions, modes of convergences, Borel-Cantelli Lemma, Central Limit Theorem, Law of Large numbers
Convergence Theorems in Markov Chains
- W. Feller: Introduction to Probability Theory and ins Applications Vol.I & Vol. II (Wiley)
- S. M. Ross: Introduction to Probability Models (AP)
- Hoel, Port & Stone: Introduction to Stochastic Processes (HMC)
- S. M. Ross: Stochastic Processes (Wiley)