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Markov renewal theory

Published online by Cambridge University Press:  01 July 2016

Erhan Çinlar
Erhan Çinlar*
Affiliation:
Northwestern University, Evanston, Illinois
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Extract

Consider a stochastic process X(t) (t ≧ 0) taking values in a countable state space, say, {1, 2,3, …}. To be picturesque we think of X(t) as the state which a particle is in at epoch t. Suppose the particle moves from state to state in such a way that the successive states visited form a Markov chain, and that the particle stays in a given state a random amount of time depending on the state it is in as well as on the state to be visited next. Below is a possible realization of such a process.

Type
Research Article
Information
Advances in Applied Probability , Volume 1 , Issue 2 , Autumn 1969 , pp. 123 - 187
Copyright
Copyright © Applied Probability Trust 

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