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We provide exact large-time equivalents of the density and upper tail distributions of the exponential functional of a subordinator in terms of its Laplace exponents. This improves previous results on the logarithmic asymptotic behaviour of the upper tail. Since the results in their general form remain rather abstract, we study some fairly common situations in detail to see how the behavior near 0 of the Lévy measure of the subordinator influences the asymptotics of the density and upper tail distributions. Several examples of applications are then discussed.

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Precise Asymptotics for the Density and the Upper Tail of Exponential Functionals of Subordinators

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  • 发表日期：

    2025年

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  • Bénédicte Haas

摘要

We provide exact large-time equivalents of the density and upper tail distributions of the exponential functional of a subordinator in terms of its Laplace exponents. This improves previous results on the logarithmic asymptotic behaviour of the upper tail. Since the results in their general form remain rather abstract, we study some fairly common situations in detail to see how the behavior near 0 of the Lévy measure of the subordinator influences the asymptotics of the density and upper tail distributions. Several examples of applications are then discussed.