Potentials of stable processes

Andreas Kyprianou, A. R. Watson

Research output: Chapter in Book/Report/Conference proceedingChapter

2 Citations (Scopus)
110 Downloads (Pure)

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.
Original languageEnglish
Title of host publicationSeminaire de Probabilites XLV1
EditorsCatherine Donati-Martin, Antoine Lejay, Alain Roualt
Place of PublicationSwitzerland
PublisherSpringer
Pages333 - 344
Number of pages12
ISBN (Electronic)978-3-319-11970-0
DOIs
Publication statusPublished - 30 Oct 2014

Publication series

NameSeminaire de Probabilites
PublisherSpringer
Volume2123
ISSN (Print)0720-8766

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Cite this

Kyprianou, A., & Watson, A. R. (2014). Potentials of stable processes. In C. Donati-Martin, A. Lejay, & A. Roualt (Eds.), Seminaire de Probabilites XLV1 (pp. 333 - 344). (Seminaire de Probabilites; Vol. 2123). Switzerland: Springer. https://doi.org/10.1007/978-3-319-11970-0_12