Suprema of Lévy processes

• Mateusz Kwaśnicki ^[2] ; Jacek Małecki ^[1] ; Michał Ryznar ^[1]
  1. [1] Wrocław University of Technology

     Wrocław University of Technology

     Breslavia, Polonia

     
  2. [2] Wroclaw University of Technology and Polish Academy of Science
• Localización: Annals of probability: An official journal of the Institute of Mathematical Statistics, ISSN 0091-1798, Vol. 41, Nº. 3, 2, 2013, págs. 2047-2065
• Idioma: inglés
• DOI: 10.1214/11-AOP719
• Texto completo no disponible (Saber más ...)
• Resumen

  • In this paper we study the supremum functional Mt=sup0≤s≤tXs, where Xt, t≥0, is a one-dimensional Lévy process. Under very mild assumptions we provide a simple, uniform estimate of the cumulative distribution function of Mt. In the symmetric case we find an integral representation of the Laplace transform of the distribution of Mt if the Lévy–Khintchin exponent of the process increases on (0,∞).