Potentials of stable processes

Andreas Kyprianou; A. R.  Watson

doi:10.1007/978-3-319-11970-0_12

Potentials of stable processes

Andreas Kyprianou, A. R. Watson

University of Zurich

Research output: Chapter or section in a book/report/conference proceeding › Book chapter

5 Citations (SciVal)

158 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 language	English
Title of host publication	Seminaire de Probabilites XLV1
Editors	Catherine Donati-Martin, Antoine Lejay, Alain Roualt
Place of Publication	Switzerland
Publisher	Springer
Pages	333 - 344
Number of pages	12
ISBN (Electronic)	978-3-319-11970-0
DOIs	https://doi.org/10.1007/978-3-319-11970-0_12
Publication status	Published - 30 Oct 2014

Publication series

Name	Seminaire de Probabilites
Publisher	Springer
Volume	2123
ISSN (Print)	0720-8766

Access to Document

10.1007/978-3-319-11970-0_12

Kyprianou-Watson (2015) Potentials of stable processes
The final publication is available at Springer via http://dx.doi.org/10.1007/978-3-319-11970-0_12
Accepted author manuscript, 145 KB

Cite this

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AU - Watson, A. R.

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AB - 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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Potentials of stable processes

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Self Similarity and Stable Processes

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Potentials of stable processes

Abstract

Publication series

Access to Document

Other files and links

Fingerprint

Projects

Self Similarity and Stable Processes

Real-Valued Self-Similar Markov Processes and their Applications

Cite this