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=21653
Markov chain, non-decomposable. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Markov_chain,_non-decomposable&oldid=21653
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