Uniform asymptotics for compound Poisson processes with regularly varying jumps and vanishing drift

B. Kamphorst, B. Zwart

Abstract

This paper addresses heavy-tailed asymptotics of functionals of a class of spectrally one-sided L\'evy process that remain valid in a near-critical regime. This complements recent similar results that have been obtained for the all-time supremum of such processes. Specifically, we consider local asymptotics of the all-time supremum, the supremum of the process until exiting $[0,\infty)$, the maximum jump until that time, and the time it takes until exiting $[0,\infty)$. The proofs rely, among other things, on properties of scale functions. Keywords: compound Poisson process, M/G/1 queue, heavy traffic, large deviations, uniform asymptotics, first passage time, supremum
Original language English s.n. 35 Published - 2015

Publication series

Name arXiv 1510.06955 [math.PR]

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