UNIVERSITY OF MADRAS
B.Sc. DEGREE COURSE IN STATISTICS
SEMESTER SYSTEM WITH CREDITS
(Effective from the Academic Year 2003-2004)

SYLLABUS

Semester VI - Application Oriented Subject II - Stochastic Processes and Their Applictions

UNIT - 1:

Basic Concepts : Definition and examples of stochastic process, classification of general stochastic processes into discrete! continuous time, discrete / continuous state spaces, types of stochastic processes, elementary problems.

UNIT - 2:

Markov chains : Definition and examples of Markov chain, Transition Probability Matrix, classification of states, recurrence, simple problems

UNIT - 3:

Basic limit theorem of Markov chain (statement only), stationary probability distribution, applications.

UNIT - 4:

Continuous Time Markov chain : Pure birth process and Poisson process, Birth and Death process, problems.

UNIT - 5:

Branching process : Deiinition and examples of discrete time branching process, probability generating function, mean and variance, probability of extinction, problems.

BOOKS FOR REFERENCE

Karlin, S. and Taylor, H.M. (1975): A first course in Stochastic processes, Academic press.
Hoel, P.M.G., Port, S.C. and Stone, C.J. (1991): Introduction to Stochastic processes, Universal Book Stall.
Parzen, E. (1962): Stochastic processes, Holden-Day.
Cinlar, B. (1975) Introduction to Stochastic processes, Prentice Hall.
Adke, S.R. and Manjunath, S.M. (1984): An introduction to Finite Markov Processes, Wiley Eastern.
Medhi, J. (1996): Stochastic processes, New Age International (p) Ltd.
Ross, S.M. (1983): Stochastic processes, John Wiley.
Taylor, H.M. and Karlin, S. (1999): Stochastic Modelling, Academic press.