Suprema of L\'evy processes
Abstract
In this paper we study the supremum functional Mt=0 s tXs, where Xt, t0, is a one-dimensional L\'evy 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 L\'evy-Khintchin exponent of the process increases on (0,∞).
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