# On exit time of stable processes

Abstract : We study the exit time $\tau=\tau_{(0,\infty)}$ for 1-dimensional strictly stable processes and express its Laplace transform at $t^\alpha$ as the Laplace transform of a positive random variable with explicit density. Consequently, $\tau$ satisfies some multiplicative convolution relations. For some stable processes, e.g. for the symmetric $\frac23$-stable process, explicit formulas for the Laplace transform and the density of $\tau$ are obtained as an application.
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https://hal.archives-ouvertes.fr/hal-00605083
Contributor : Piotr Graczyk <>
Submitted on : Thursday, June 30, 2011 - 3:08:53 PM
Last modification on : Monday, March 9, 2020 - 6:15:53 PM
Document(s) archivé(s) le : Saturday, October 1, 2011 - 2:27:23 AM

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• HAL Id : hal-00605083, version 1

### Citation

Piotr Graczyk, Tomasz Jakubowski. On exit time of stable processes. 2011. ⟨hal-00605083⟩

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