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Stationary Distributions of a Markov Chain

In: Classical and Spatial Stochastic Processes

Author

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  • Rinaldo B. Schinazi

    (University of Colorado, Department of Mathematics)

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.

Suggested Citation

  • Rinaldo B. Schinazi, 1999. "Stationary Distributions of a Markov Chain," Springer Books, in: Classical and Spatial Stochastic Processes, chapter 0, pages 43-71, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4612-1582-0_2
    DOI: 10.1007/978-1-4612-1582-0_2
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