Abstract
In this chapter, we discuss some natural generalisations of the asymptotic results presented in Chaps. 8–11. We also describe the features of the asymptotic recurrent algorithms of phase space reduction for perturbed semi-Markov processes of the birth–death type. Finally, we give numerical examples illustrating the above algorithms and their applications to the asymptotic analysis of distributions and expectations of hitting times for singularly perturbed semi-Markov processes. This chapter includes three sections.
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References
Kallenberg, O. (2021). Foundations of Modern Probability. Third Edition. Probability Theory and Stochastic Modelling, 99, Springer, xii+946 pp.
Silvestrov D.S. (2004). Limit Theorems for Randomly Stopped Stochastic Processes. Probability and Its Applications, Springer, London, xvi+398 pp.
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Silvestrov, D. (2022). Generalisations and Examples of Limit Theorems for Hitting Times. In: Perturbed Semi-Markov Type Processes I. Springer, Cham. https://doi.org/10.1007/978-3-030-92403-4_12
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DOI: https://doi.org/10.1007/978-3-030-92403-4_12
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