Identifying Markov chains with a given invariant measure

Phil Pollett

Abstract: Consider the following problem: given a stable, conservative q-matrix Q over a denumerable state-space S, together with a subinvariant measure m for Q, determine all Q-processes for which m is an invariant measure. We shall review recent work on this problem, giving particular attention to the case when Q is a single-exit q-matrix. We shall also study the case when S consists of a single absorbing state 0 and an irreducible class C, and consider the problem of constructing Q-processes for which a given measure m is m-invariant on C.

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Last modified: 19th August 1999