DESCRIPTION OF COURSES
AS 607 STOCHASTIC PROCESSES (3L+0P) II
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.
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.
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.
Renewal process: renewal process when time is discrete and continuous. Renewal function and renewal density. Statements of elementary renewal theorem and Key renewal theorem.
Elements of queuing processes: queues in series, queuing networks. Applications of queuing theory.
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.