Computing Expected Transition Events in Reducible Markov Chains

Authors:
Brian D. Ewald;Jeffrey Humpherys;Jeremy M. West
Affiliations:
ewald@math.fsu.edu;jeffh@math.byu.edu and jwest@math.byu.edu;-
Venue:
SIAM Journal on Matrix Analysis and Applications
Year:
2009

Citing 6
Cited 0

Topics in matrix analysis

Topics in matrix analysis
Applied numerical linear algebra

Applied numerical linear algebra
Matrix analysis and applied linear algebra

Matrix analysis and applied linear algebra
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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.