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

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  • Kamphorst, Bart
  • Zwart, Bert

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.

Suggested Citation

  • Kamphorst, Bart & Zwart, Bert, 2019. "Uniform asymptotics for compound Poisson processes with regularly varying jumps and vanishing drift," Stochastic Processes and their Applications, Elsevier, vol. 129(2), pages 572-603.
    • Handle: RePEc:eee:spapps:v:129:y:2019:i:2:p:572-603
    DOI: 10.1016/j.spa.2018.03.012
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    References listed on IDEAS

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