Abstract
In the present chapter we evolve a constructive method that provides limiting results in the form of a generalized Rényi theorem. This allows us to consider the case where the d.f. F of summands in the underlying geometric sum may vary together with parameter q of the corresponding geometric distribution. Although the limiting results are qualitative, they can easily be stated in the form of quantitative bounds. This is partly done in this chapter but generally this problem will be solved in the following chapter. Applications to the heavy traffic regime in queueing and to rare excursions of general Markov chains are considered; they provide practice and help to illuminate the concepts and methods. Applications to insurance and reliability will be discussed in Chapters 6 and 7 correspondingly.
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Kalashnikov, V. (1997). Generalized Rényi Theorem. In: Geometric Sums: Bounds for Rare Events with Applications. Mathematics and Its Applications, vol 413. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-1693-2_3
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DOI: https://doi.org/10.1007/978-94-017-1693-2_3
Publisher Name: Springer, Dordrecht
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