# Markov chain, non-decomposable

From Encyclopedia of Mathematics

A Markov chain whose transition probabilities have the following property: For any states and there is a time such that . The non-decomposability of a Markov chain is equivalent to non-decomposability of its matrix of transition probabilities for a discrete-time Markov chain, and of its matrix of transition probability densities , for a continuous-time Markov chain. The state space of a non-decomposable Markov chain consists of one class of communicating states (cf. Markov chain).

#### Comments

Cf. also Markov chain and Markov chain, decomposable for references.

**How to Cite This Entry:**

Markov chain, non-decomposable.

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Markov_chain,_non-decomposable&oldid=14296

This article was adapted from an original article by B.A. Sevast'yanov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article