On exit time of stable processes

Details On exit time of stable processes On exit time of stable processes

2011-03-22

arxiv.org/abs/1103.4251v1

Mathematics

Probability

Scientific paper

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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