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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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