Which Markov chains have a given invariant measure?

Phil Pollett

Abstract: I will consider the following problem: given a stable, conservative q-matrix Q of transition rates 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. I will review recent work on this problem, giving particular attention to the case when Q is a single-exit q-matrix. I will also examine 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. [The latter is joint work with Hanjun Zhang.]

Acknowledgement: This work is supported by the ARC Centre of Excellence for Mathematics and Statistics of Complex Systems

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Last modified: 28th March 2005