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On exit time of stable processes


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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hal-00605083 , version 1 (30-06-2011)


  • HAL Id : hal-00605083 , version 1


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