Time changes of Markov chains

A. O. Pittenger

Stochastic Processes and their Applications, 1982, vol. 13, issue 2, 189-199

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.

Date: 1982
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