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