Resumen de Suprema of Lévy processes

Mateusz Kwasnicki, Jacek Malecki, Michal Ryznar

• 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,∞).