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Time changes of Markov chains

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  • Pittenger, A. O.

Abstract

An increasing sequence of random times {Tn, n [greater-or-equal, slanted] 0} is called a Markov time change if {X(Tn)} is a new Markov chain. If the {Tn} satisfy certain 'operational' requirements such as conditional independence of the Tn-past and Tn-future given X(Tn), then there is an equivalent, algebraic description of the {Tn} in terms of a triple (T0,S,[Gamma]), where T0 and S are splitting times with respect to a set [Gamma]. A further assumption on [Gamma] makes it easy to check that a triple will generate a Markov time change, and it is shown that processes such as last exit processes and excision processes satisfy this assumption.

Suggested Citation

  • Pittenger, A. O., 1982. "Time changes of Markov chains," Stochastic Processes and their Applications, Elsevier, vol. 13(2), pages 189-199, August.
    • Handle: RePEc:eee:spapps:v:13:y:1982:i:2:p:189-199
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    Cited by:

    1. Barsotti, Flavia & De Castro, Yohann & Espinasse, Thibault & Rochet, Paul, 2014. "Estimating the transition matrix of a Markov chain observed at random times," Statistics & Probability Letters, Elsevier, vol. 94(C), pages 98-105.

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