Suprema and sojourn times of Lévy processes with exponential tails

Research output: Contribution to journalArticlepeer-review

15 Scopus citations


We study the tail behaviour of the supremum of sample paths of Lévy process with exponential tail of the Lévy measure. Our approach is based on the theory of sojourn times developed by S. Berman. It allows us to compute the value of the limit of the ratio P(sup0 ≤ t ≤ l X(t) > x)/p(x, ∞) as x → ∞, where ρ is the Lévy measure of the process.

Original languageEnglish
Pages (from-to)265-283
Number of pages19
JournalStochastic Processes and their Applications
Issue number2
StatePublished - 16 Jun 1997


  • Exponential distributions
  • Lévy process
  • Sojourn times

ASJC Scopus subject areas

  • Statistics and Probability
  • Modeling and Simulation
  • Applied Mathematics


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