Perturbed Semi-Markov Processes and Reduction of Phase Space

Dmitrii Silvestrov
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Dmitrii Silvestrov: Stockholm University, Department of Mathematics

Chapter Chapter 9 in Perturbed Semi-Markov Type Processes I, 2022, pp 219-259 from Springer

Abstract: Abstract In this chapter, we present models of regularly and singularly perturbed semi-Markov processes and formulate basic perturbation conditions and asymptotic comparability conditions based on the notion of a complete family of asymptotically comparable functions. We also describe asymptotic procedures of removing virtual transitions and one-state reducing the phase space, and an asymptotic recurrent phase space reduction algorithm for perturbed semi-Markov processes. These procedures and algorithm are provided by explicit formulas for recalculating normalisation functions, Laplace transforms for limit distributions, and limit expectations appearing in perturbation conditions for semi-Markov processes with reduced phase space. This chapter includes four sections.

Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-030-92403-4_9

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DOI: 10.1007/978-3-030-92403-4_9

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