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Markov intervention of chance, and limit theorems. (English. Russian original) Zbl 0595.60029
Math. USSR, Sb. 54, 161-183 (1986); translation from Mat. Sb., Nov. Ser. 126(168), No. 2, 172-193 (1985).
A random process \((\xi_ t)_{t>0}\) with some measurable state space, and an increasing sequence of stopping times \((\tau_ k)_ 0^{\infty}\) are considered. The process is assumed to have the Markov property with respect to every \(\tau_ k\), and the Markov chain \((\xi (\tau_ k))_ 0^{\infty}\) is supposed to be homogeneous and Harris recurrent.
In terms of stationary probabilities of this chain, formulae for the final probabilities of the process \((\xi_ t)\) are derived. For additive functionals of the process some renewal theorems and a variant of the central limit theorem are proved.
Reviewer: B.P.Kharlamov

MSC:
60F05 Central limit and other weak theorems
60G10 Stationary stochastic processes
60K15 Markov renewal processes, semi-Markov processes
60G40 Stopping times; optimal stopping problems; gambling theory
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