Limit theorems and proximity estimates for summation schemes on Markov chains. (Russian) Zbl 0638.60075

Anisimov, V. V.; Pushkin, S. G.

Teor. Veroyatn. Mat. Stat., Kiev 37, 7-16 (1987).

In a scheme of series, conditions of weak convergence of finite- dimensional distributions and measures in Skorokhod space \({\mathcal D}_{[0,T]}\) to nonhomogeneous processes with independent increments for step processes of sums of nonhomogeneous random variables on a homogeneous Markov chain, which satisfies the asymptotic uniform strong mixing condition, are obtained.
The estimates of the convergence rate to the Poisson flows are obtained for the flows of “rare” indicators. As a consequence a theorem of the limiting behaviour of the time of staying of a honhomogeneous semi-Markov process in a fixed subset of states is proved.

Reviewer: V.V.Anisimov

MSC:

60J10	Markov chains (discrete-time Markov processes on discrete state spaces)
60F17	Functional limit theorems; invariance principles
60B10	Convergence of probability measures
60K15	Markov renewal processes, semi-Markov processes

Keywords:

weak convergence of finite-dimensional distributions; asymptotic uniform strong mixing condition; convergence rate; Poisson flows; semi-Markov process