Ergodic Theorems for Regularly Perturbed Alternating Regenerative Processes

Dmitrii Silvestrov
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Dmitrii Silvestrov: Stockholm University, Department of Mathematics

Chapter Chapter 4 in Perturbed Semi-Markov Type Processes II, 2022, pp 69-91 from Springer

Abstract: Abstract In this chapter, we present individual ergodic theorems for perturbed alternating regenerative processes modulated by regularly perturbed two-state semi-Markov processes (shortly referred as regularly perturbed alternating regenerative processes). This is the case where both regime switching probabilities for perturbed modulating semi-Markov processes converge to positive limiting values, as ε → 0. We also present ergodic theorems for semi-regularly perturbed alternating regenerative processes. This is case where one regime switching probability for perturbed modulating semi-Markov processes converges to a positive limiting value, while another one converges to 0, as ε → 0. This chapter includes four sections.

Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-030-92399-0_4

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DOI: 10.1007/978-3-030-92399-0_4

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