**DESCRIPTION OF COURSES**

**AS 607 STOCHASTIC PROCESSES (3L+0P) II**

**Objective**

This course aims at describing some advanced level topics in this area of research with a very strong potential of applications. This course also prepares students for undertaking research in this area and helps them for applications of this important subject to agricultural sciences.

**Theory**

UNIT I

Basics of stochastic processes. Classification according to state space and time domain. Finite and countable state Markov chains, time-homogeneity, Chapman-Kolmogorov equations, marginal distribution and finite dimensional distributions. Classification of Markov chain. 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 gamblers ruin problem.

UNIT II

Birth and death processes like pure birth process, linear birth and death process, immigration- birth-death process. Discrete state continuous time Markov process: Kolmogorov difference - differential equations. Pure birth process (Yule-Fury process). Immigration-Emigration process. Linear growth process, pure death process.

UNIT III

Renewal process: renewal process when time is discrete and continuous. Renewal function and renewal density. Statements of elementary renewal theorem and Key renewal theorem.

UNIT IV

Elements of queuing processes: queues in series, queuing networks. Applications of queuing theory.

UNIT V

Epidemic processes: simple deterministic and stochastic epidemic model. General epidemic models: Kermack and McKendrick’s threshold theorem. Recurrent epidemics. Chain binomial models. Diffusion processes. Diffusion limit of a random walk and Discrete branching process. Forward and backward Kolmogorov diffusion equations and their applications.

**Suggested Readings**

- Adke, S.R. and Manjunath, S.M. 1984.
*An Introduction to Finite Markov Processes*. John Wiley. - Bailey, N.T.J. 1964.
*Elements of Stochastic Processes with Applications to the Natural Sciences*. Wiley Eastern Ltd. - Bartlett, M.S. 1955.
*Introduction to Stochastic Processes*. Cambridge University Press. - Basawa, I.V. and Prakasa Rao, B.L.S. 1980.
*Statistical Inference for Stochastic Processes*. Academic Press. - Bharucha Reid, A.T. 1960.
*Elements of the Theory of Markov Processes and their Applications*. McGraw Hill. - Bhat, B.R. 2000.
*Stochastic Models*:*Analysis and Applications*. New Age International India. - Cox, D.R. and Miller, H.D. 1965.
*The Theory of Stochastic Processes*. Methuen. Draper, N.R. and Smith, H. 1981.*Applied Regression Analysis*. Wiley Eastern Ltd. France, J. and Thornley, J.H.M. 1984.*Mathematical Models in Agriculture*. Butterworths. - Karlin,S. and Taylor, H.M. 1975.
*A First Course in Stochastic Processes*. Vol. 1. Academic Press. - Lawler, G.F. 1995.
*Introduction to Stochastic Processes*. Chapman and Hall. Medhi, J. 2001.*Stochastic Processes*. Wiley Eastern Ltd. - Parzen, E. 1962.
*Stochastic Processes.*Holden-Day, San Francisco. Prabhu, N.U. 1965.*Stochastic Processes*. Macmillan. - Prakasa Rao, B.L.S. and Bhat, B.R. 1996.
*Stochastic Processes and Statistical Inference*. New Age International Publisher. - Ratkowsky, D.A. 1983.
*Nonlinear Regression Modelling: a Unified Practical Approach*. Marcel Dekker. Ratkowsky, D.A. 1990.*Handbook of Nonlinear Regression Models*. Marcel Dekker. - Seber, G.A.F. and Wild, C.J. 1989.
*Non-linear Regression*. John Wiley.