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

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.

MSC:

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