Abstract
In this chapter, the results obtained in previous chapters are illustrated by applications to geometric type random sums. Necessary and sufficient conditions of convergence in distribution for first-rare-event times represented by geometric type random sums are formulated. Also, necessary and sufficient conditions of weak convergence for non-ruin distribution functions in the models of stable and diffusion approximations for perturbed risk processes are given. In this chapter includes two sections.
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References
Asmussen, S. (2000). Ruin probabilities. Advanced Series on Statistical Science & Applied Probability, 2. World Scientific, River Edge, NJ, xii+385 pp.
Asmussen, S., Albrecher, H. (2010). Ruin Probabilities. Second edition, Advanced Series on Statistical Science & Applied Probability, 14, World Scientific, Hackensack, NJ, xviii+602 pp.
Feller, W. (1971). An Introduction to Probability Theory and Its Applications, Vol. II. (Second edition, Wiley Series in Probability and Statistics, Wiley, New York, xxiv+669 pp. (First edition in 1966).
Kovalenko, I.N. (1965). On the class of limit distributions for thinning flows of homogeneous events. Litov. Mat. Sbornik, 5, 569–573.
Loève, M. (1977). Probability Theory. I. Fourth edition. Graduate Texts in Mathematics, 45, Springer, New York, xvii+425 pp. (First edition in 1955).
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Silvestrov, D. (2022). First-Rare-Event Times for Perturbed Risk Processes. In: Perturbed Semi-Markov Type Processes I. Springer, Cham. https://doi.org/10.1007/978-3-030-92403-4_5
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DOI: https://doi.org/10.1007/978-3-030-92403-4_5
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