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)

166 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

@inbook{1b2093248eb64e918a457a8088d4d285,

title = "Potentials of stable processes",

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.",

author = "Andreas Kyprianou and Watson, \{A. R.\}",

year = "2014",

month = oct,

day = "30",

doi = "10.1007/978-3-319-11970-0\_12",

language = "English",

series = "Seminaire de Probabilites",

publisher = "Springer",

pages = "333 -- 344",

editor = "Catherine Donati-Martin and Antoine Lejay and Alain Roualt",

booktitle = "Seminaire de Probabilites XLV1",

}

TY - CHAP

T1 - Potentials of stable processes

AU - Kyprianou, Andreas

AU - Watson, A. R.

PY - 2014/10/30

Y1 - 2014/10/30

N2 - 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.

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.

UR - http://dx.doi.org/10.1007/978-3-319-11970-0_12

UR - http://link.springer.com/chapter/10.1007/978-3-319-11970-0_12/fulltext.html

UR - http://arxiv.org/pdf/1312.1222.pdf

UR - https://www.scopus.com/pages/publications/84927129135

U2 - 10.1007/978-3-319-11970-0_12

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

M3 - Book chapter

T3 - Seminaire de Probabilites

SP - 333

EP - 344

BT - Seminaire de Probabilites XLV1

A2 - Donati-Martin, Catherine

A2 - Lejay, Antoine

A2 - Roualt, Alain

PB - Springer

CY - Switzerland

ER -

Potentials of stable processes

Abstract

Publication series

Access to Document

Other files and links

Fingerprint

Self Similarity and Stable Processes

Real-Valued Self-Similar Markov Processes and their Applications

Cite this

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