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arXiv · 1312.1222

Potentials of stable processes

A. E. Kyprianou·A. R. Watson
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Abstract

For a stable process, we give an explicit formula for the potential measure of the process killed outside a bounded interval and the joint law of the overshoot, undershoot and undershoot from the maximum at exit from a bounded interval. We obtain the equivalent quantities for a stable process reflected in its infimum. The results are obtained by exploiting a simple connection with the Lamperti representation and exit problems of stable processes.

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A. E. Kyprianou, A. R. Watson. 2013-12-04. Potentials of stable processes. https://doi.org/10.1007/978-3-319-11970-0_12

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