Time changes of Markov chains

AbstractAn increasing sequence of random times {Tn, n ⩾ 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,Γ), where T0 and S are splitting times with respect to a set Γ. A further assumption on Γ 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