Mathematics – Probability
Scientific paper
2008-06-07
Mathematics
Probability
15 pages, 1 table. Added numerical analysis and changed formatting. Fixed several errors
Scientific paper
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.
Ewald Brian D.
Humpherys Jeffrey
West Jeremy
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