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# Osmania University - M.Sc. STATISTICS - 2 - ST 202 U : Paper II: Stochastic Processes

 Posted Date: 23-Oct-2008 Last Updated: 23-Oct-2008 Category: Syllabus Author: Nitin Member Level: Diamond Points: 2

ST 202 U : Paper II: Stochastic Processes

UNIT – I
Introduction to stochastic processes; classification of stochastic process according to state-space and time-domain. Finite and countable state Markov chains; time-homogeneity; Chapman-Kolmogorov equations; marginal distribution and finite – dimensional distribution; classification of states of a Markov chain – recurrent, positive recurrent, null - recurrent and transient states. Period of a state.

UNIT – II
Canonical form of transition probability matrix of a Markov chain. Fundamental matrix; probabilities of absorption from transient states into recurrent classes, in a finite Markov Chain; mean time for absorption. Ergodic state and ergodic chain. Stationary distribution of a Markov chain. Existence and evaluation of stationary distribution. Random walk and gambler’s ruin problem.

UNIT – III
Discrete state-space, continuous time Markov Processes – Kolmogorov difference - differential equations. Poisson process and its properties. Birth and Death Process, application in queuing. Pure Birth and pure Death processes.
Weiner process as limit of random walk. First passage time of the process.

UNIT – IV
Renewal process, elementary renewal theorem and its applications. Statement and uses of Key – renewal theorem. Residual life time. Branching process – Galton-Watson branching process, mean and variance of size of nth generation; probability of ultimate extinction of a branching process – fundamental theorem of Branching process – Examples.

REFERENCES

1. Medhi,J. (1982) : Stochastic Processes – Wiley Eastern
2. Karlin, S. and Taylor, H.M. (1975) : A First Course in Stochastic Processes, Vol. I, Academic Press.

ADDITIONAL REFERENCES

1. Bhat, B.R.(2000) : Stochastic Models : Analysis and applications – New Age International India.
2. Basu, A.K.(2003): Introduction to Stochastic Process, Narosa Publishing House.

Reference: https://osmania.ac.in

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