Weak convergence of semi-Markov random evolutions in an averaging scheme. (English. Russian original) Zbl 0747.60025

Korolyuk, V. S.; Svishchuk, A. V.

Theory Probab. Math. Stat. 42, 61-71 (1991); translation from Teor. Veroyatn. Mat. Stat., Kiev 42, 53-64 (1990).

This is a continuation of the authors’ previous work on semi-Markov random evolutions [see e.g., Ukr. Math. J. 41, No. 2, 147-153 (1989); translation from Ukr. Mat. Zh. 41, No. 2, 163-170 (1989; Zbl 0678.60085)]. In the present paper, the tightness of a family of semi- Markov random evolutions with an underlying uniformly ergodic homogeneous Markov chain is proved for both the original process and some associated lumped process.

Reviewer: M.Iosifescu (Bucureşti)

MSC:

60F05	Central limit and other weak theorems
60K15	Markov renewal processes, semi-Markov processes
93E03	Stochastic systems in control theory (general)

Keywords:

semi-Markov random evolutions; tightness; uniformly ergodic homogeneous Markov chain

Citations:

Zbl 0716.60098; Zbl 0678.60085