Unit 1

Random variables and Stochastic Processes: Probability generating function-mean and variance, Laplace transform of probability distributions, geometric and exponential distributions, sums of random number of continuous random variables, Geometric and Exponential distributions and properties.

Unit 2

Stochastic processes, Introduction, Classification of stochastic processes, statistical properties such as mean, variance, auto covariance and auto correlation, properties, Weak stationary, Strict stationary and non-stationary processes and examples, Mean ergodic processes.

Unit 3

Markov Chains: Definition of Markov Chain and examples, higher transition probabilities, Classification of states and chains, Determination of higher transition probabilities-limiting behavior, stability of a Markov System-Computation of equilibrium probabilities, Markov chains with denumerable number of states, Reducible Markov chains.

Unit 4

Counting processes, Poisson Process: Definition, Poisson process, properties and related distributions, Generalization of Poisson process, Continuous time Markov chains, Birth and death process, Markov process with discrete state space, Chapman-Kolmogorov equations, limiting distributions.

Unit 5

Applications in stochastic models, Queuing systems and models, Birth and death process in queueing theory, M/M/1 and M/M/s models with finite and infinite system capacity.

Course outcomes
CO1: Understand to Illustrate and formulate fundamental probability distribution and density functions, as well as functions of random variables
CO2: Able to understand the concept of Stochastic processes, various classifications, Statistical proprieties and understand about weak stationary and strict stationary processes and ergodic processes.
CO3: Ability to understand discrete time Markov chains and their applications
CO4: Understanding the Poisson processes and their applications in stochastic modelling CO5: Understand the applications of stochastic processes and use of that in in day to day life

Text Book:

• J. Medhi, Stochastic Processes, New Age International Publishers.

References:

1. S. Karlin & H.M. Taylor, A First course in Stochastic processes, Academic press, 1975. Sheldon M. Ross, Stochastic Processes, second Edition, John Wiley and Sons, Inc.2004 William Feller, An
2. Introduction to Probability Theory and its Applications, Vo1.I, Wiley. Sheldon M Ross, Simulation, 4th edition, Elsevier.
3. Taha, H. (1995), Operations Research: An Introduction, Prentice- Hall India.