Convergence of switching reward processes. (English. Ukrainian original) Zbl 0990.60023

Anisimov, V. V.

Theory Probab. Math. Stat. 63, 1-11 (2001); translation from Teor. Jmovirn. Mat. Stat. 63, 3-12 (2000).

The author investigates the convergence in Skorokhod \(J\)-topology of the accumulation processes constructed by sums of conditionally independent random variables or processes with conditionally independent increments on trajectories of switching processes. The recurrent semi-Markov processes and the recurrent semi-Markov processes with additional Markov switching are considered. Convergence in \(J\)-topology of the considered accumulation processes with switching to the non-homogeneous process with independent increments is proved. Applications to the accumulation processes in the queueing models are presented.

Reviewer: A.D.Borisenko (Kyïv)

MSC:

60F15	Strong limit theorems
60K15	Markov renewal processes, semi-Markov processes
60G51	Processes with independent increments; Lévy processes

Keywords:

\(J\)-convergence; accumulation processes with switching; conditionally independent random variables; recurrent semi-Markov process; non-homogeneous processes with independent increments