Multi-alternating Regenerative Processes with Semi-Markov Modulation

Dmitrii Silvestrov
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Dmitrii Silvestrov: Stockholm University, Department of Mathematics

Chapter Chapter 11 in Coupling and Ergodic Theorems for Semi-Markov-Type Processes II, 2025, pp 427-454 from Springer

Abstract: Abstract In Chap. 11 , we present ergodic theorems with explicit upper bounds for convergence rates for multi-alternating regenerative processes with semi-Markov modulation. These processes generalize naturally both regenerative and semi-Markov processes. We introduce multi-alternating regenerative processes modulated by semi-Markov processes and give renewal-type equations for distributions of multi-alternating regenerative processes and relations connecting their distributions and the distributions of accompanying Markov processes for modulating semi-Markov processes. We give two series of ergodic theorems with explicit power and exponential upper bounds for convergence rates for multi-alternating regenerative processes modulated by semi-Markov processes with atoms and for multi-alternating regenerative processes modulated by semi-Markov processes admitting artificial regeneration.

Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-031-89315-5_11

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DOI: 10.1007/978-3-031-89315-5_11

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