Stationary Distributions of a Markov Chain

Rinaldo B. Schinazi
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Rinaldo B. Schinazi: University of Colorado, Department of Mathematics

Chapter II in Classical and Spatial Stochastic Processes, 1999, pp 43-71 from Springer

Abstract: Abstract What is in this chapter? Let X n be the state of a Markov chain at time n. Assume that X0, the initial state of the chain, is distributed according to a distribution π. That is, assume that the probability that X0 is in state i is π(i). Can we find a distribution π such that if X0 has distribution π then X n , for all times n, also has distribution π? Such a distribution is said to be stationary for the chain. This chapter deals with the existence of and the convergence to stationary distributions.

Date: 1999
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DOI: 10.1007/978-1-4612-1582-0_2

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