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Generalisations of Limit Theorems for First-Rare-Event Times

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Perturbed Semi-Markov Type Processes I

Abstract

In this chapter, we generalise the results of Chap. 2 to some modifications of first-rare-event times and processes. The relationship between first-rare-event times and hitting times is also clarified. In this chapter includes two 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.

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  • 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 of Limit Theorems for First-Rare-Event Times. In: Perturbed Semi-Markov Type Processes I. Springer, Cham. https://doi.org/10.1007/978-3-030-92403-4_4

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