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arXiv · 0806.1291

Computing expected transition events in reducible Markov chains

Brian D. Ewald·Jeffrey Humpherys·Jeremy West
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Abstract

We present a closed-form, computable expression for the expected number of times any transition event occurs during the transient phase of a reducible Markov chain. Examples of events include time to absorption, number of visits to a state, traversals of a particular transition, loops from a state to itself, and arrivals to a state from a particular subset of states. We give an analogous expression for time-average events, which describe the steady-state behavior of reducible chains as well as the long-term behavior of irreducible chains.

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Brian D. Ewald, Jeffrey Humpherys, Jeremy West. 2008-06-07. Computing expected transition events in reducible Markov chains. https://doi.org/10.1137/080726082

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