On suprema of Lévy processes with light tails

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2 Scopus citations

Abstract

Let X (t), t ≥ 0, X (0) = 0, be a Lévy process with a spectral Lévy measure ρ. Assuming that ∫- 11 | x | ρ (d x) < ∞ and the right tail of ρ is light, we show that in the presence of the Brownian component P (under(sup, 0 ≤ t ≤ 1) X (t) > u) ∼ P (X (1) > u) as u → ∞, while in the absence of a Brownian component these tails are not always comparable.

Original languageEnglish
Pages (from-to)541-573
Number of pages33
JournalStochastic Processes and their Applications
Volume120
Issue number4
DOIs
StatePublished - 1 Apr 2010

Keywords

  • Brownian motion
  • Poisson process
  • Supremum

ASJC Scopus subject areas

  • Statistics and Probability
  • Modeling and Simulation
  • Applied Mathematics

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