Periodic regeneration

Hermann Thorisson

Stochastic Processes and their Applications, 1985, vol. 20, issue 1, 85-104

Abstract: We consider stochastic processes Z = (Zt)[0,[infinity]), on a general state space, having a certain periodic regeneration property: there is an increasing sequence of random times (Sn)[infinity]0 such that the post-Sn process is conditionally independent of S0,...,Sn given (Sn mod 1) and the conditional distribution does not depend on n. Our basic condition is that the distributions , have a common component that is absolutely continuous w.r.t. Lebesgue measure. Then Z has the following time-homogeneous regeneration property: there exists a discrete aperiodic renewal process T = (Tn)[infinity]0 such that the post-Tn process is independent of T0,...,Tn and its distribution does not depend on n; this yields weak ergodicity. Further, the Markov chain (Sn mod 1)[infinity]0 has an invariant distribution [pi][0,1) and it holds that Tn+1 - Tn has finite first moment if and only if m = [integral operator] m(Ps)[pi][0,1)(ds)

Keywords: periodicity; regeneration; renewal; theory; ergocity (search for similar items in EconPapers)
Date: 1985
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