Potentials of stable processes

A. E. Kyprianou; A. R. Watson

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

Potentials of stable processes

A. E. Kyprianou, A. R. Watson

The University of Manchester

Research output: Contribution to journal › Article › peer-review

32 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
Pages (from-to)	333-343
Number of pages	10
Journal	Seminaire de Probabilites
Volume	XLVI
DOIs	https://doi.org/10.1007/978-3-319-11970-0_12
Publication status	Published - 2014

Keywords

Levy processes
stable processes
reflected stable processes
hitting times
positive self-similar Markov processes
Lamperti representation
potential measures
resolvent measures

Access to Document

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

POST-PEER-REVIEW-NON-PUBLISHERS.PDFAccepted author manuscript, 145 KB

Cite this

@article{405f94c84d8d43b4960fb2851762773a,

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.",

keywords = "Levy processes, stable processes, reflected stable processes, hitting times, positive self-similar Markov processes, Lamperti representation, potential measures, resolvent measures",

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

year = "2014",

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

language = "English",

volume = "XLVI",

pages = "333--343",

journal = "Seminaire de Probabilites",

issn = "0720-8766",

publisher = "Springer Nature",

}

TY - JOUR

T1 - Potentials of stable processes

AU - Kyprianou, A. E.

AU - Watson, A. R.

PY - 2014

Y1 - 2014

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.

KW - Levy processes

KW - stable processes

KW - reflected stable processes

KW - hitting times

KW - positive self-similar Markov processes

KW - Lamperti representation

KW - potential measures

KW - resolvent measures

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

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

M3 - Article

VL - XLVI

SP - 333

EP - 343

JO - Seminaire de Probabilites

JF - Seminaire de Probabilites

SN - 0720-8766

ER -

Potentials of stable processes

Abstract

Keywords

Access to Document

Fingerprint

Cite this