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

Bart Kamphorst and Bert Zwart

Stochastic Processes and their Applications, 2019, vol. 129, issue 2, 572-603

Abstract: This paper addresses heavy-tailed large-deviation estimates for the distribution tail of functionals of a class of spectrally one-sided Lévy processes. Our contribution is to show that these estimates 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,∞), the maximum jump until that time, and the time it takes until exiting [0,∞). 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 (search for similar items in EconPapers)
Date: 2019
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Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:129:y:2019:i:2:p:572-603

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DOI: 10.1016/j.spa.2018.03.012

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