Summary of Ergodic Theorems for Regenerative Processes

Dmitrii Silvestrov
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Dmitrii Silvestrov: Stockholm University, Department of Mathematics

Chapter Chapter 2 in Coupling and Ergodic Theorems for Semi-Markov-Type Processes II, 2025, pp 33-56 from Springer

Abstract: Abstract In Chap. 2, we present the summary of coupling ergodic theorems with explicit upper bounds for convergence rates for regenerative processes obtained in the first volume. These theorems are a basis for getting ergodic theorems with explicit upper bounds for convergence rates for semi-Markov processes and multi-alternating regenerative processes with semi-Markov modulation. We give the constructive definitions of a regenerative process with a transition period and thinned regenerative processes, formulate and comment on the weighting absolute continuity condition, which plays a key role in ergodic theorems with explicit upper bounds for convergence rates, and present ergodic theorems explicit power and exponential upper bounds for convergence rates for regenerative processes.

Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-031-89315-5_2

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DOI: 10.1007/978-3-031-89315-5_2

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