Chennai Mathematical Institute


2.00-3.00 p.m., Seminar Hall
What is a Markov chain?

K. Lakshmanan Memorial Distinguished Lecture
Krishna B. Athreya
Distinguished Professor Emeritus, College of Liberal Arts and Sciences, Iowa State University, U.S.A.


A random time evolving system has the Markov property if given the present the future and the past are stochastically independent. We will discuss the four cases generated by two choices for the time index (namely positive integers or positive half line) and two choices for space(countable or general sate space). We will give many examples. The concepts of communication, irreducibility, transience, null and positive recurrence, stationary probability distributions, invariant measures, ergodic theorems and central limit theorem will be discussed. We will apply these notions to random walks and Brownian motion. If time permits the use of Markov chains for statistical estimation, ie, MCMC techniques will be outlined.