Unit 1: 

Introduction to probability theory and random process.

Unit 2: 

Markov Chains: Transistion Probability Matrices. Classification of States, Recurrence; Basic Limit Theorems. Discrete Renewal Equation, absorption Probabilities, Criteria for recurrence.

Unit 3: 

Some Queuing Models (M/G/1, G/M/1), Random Walk: Continuous Time Markov Chains : Birth process, Birth & Death processes, Differential Equations of Birth & Death Processes, Absorption.

Unit 4: 

Renewal Processes: Renewal Equations, Elementary renewal Theorem, Renewal Theorem and Applications. Generalizations and variations.

Unit 5:

Martingales : Supermartingales and Submartingales, Optional Sampling Theorem, Martingale conveyance Theorems.

1. S. Karlin, H.M. Taylor , A first course in Stochastic Processes (Academic Press 1975) 2nd Edn.
2. Battacharya of Waymiuc : Stochastic Proceese (John Wiley 1998)
3. Stirzaker, Grimrnet : Probability & Random Processes (Clarender Press 1992) U.N.
4. Bhat, Gregory Miller : Applied Stochastic Processes (Wiley Inter 2002) 3rd Edn.