Right inverses of lévy processes

Ron Doney; Mladen Savov

doi:10.1214/09-AOP515

Right inverses of lévy processes

Ron Doney, Mladen Savov

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

Abstract

We call a right-continuous increasing process Kx a partial right inverse (PRI) of a given Lévy process X if XKx = x for at least all x in some random interval [0, ζ) of positive length. In this paper, we give a necessary and sufficient condition for the existence of a PRI in terms of the Lévy triplet. © Institute of Mathematical Statistics, 2010.

Original language	English
Pages (from-to)	1390-1400
Number of pages	10
Journal	Annals of Probability
Volume	38
Issue number	4
DOIs	https://doi.org/10.1214/09-AOP515
Publication status	Published - Jul 2010

Keywords

Creeping
Excursions
Ladder height subordinator
Lévy process
Sample path behavior

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title = "Right inverses of l{\'e}vy processes",

abstract = "We call a right-continuous increasing process Kx a partial right inverse (PRI) of a given L{\'e}vy process X if XKx = x for at least all x in some random interval [0, ζ) of positive length. In this paper, we give a necessary and sufficient condition for the existence of a PRI in terms of the L{\'e}vy triplet. {\textcopyright} Institute of Mathematical Statistics, 2010.",

keywords = "Creeping, Excursions, Ladder height subordinator, L{\'e}vy process, Sample path behavior",

author = "Ron Doney and Mladen Savov",

year = "2010",

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AU - Doney, Ron

AU - Savov, Mladen

PY - 2010/7

Y1 - 2010/7

N2 - We call a right-continuous increasing process Kx a partial right inverse (PRI) of a given Lévy process X if XKx = x for at least all x in some random interval [0, ζ) of positive length. In this paper, we give a necessary and sufficient condition for the existence of a PRI in terms of the Lévy triplet. © Institute of Mathematical Statistics, 2010.

AB - We call a right-continuous increasing process Kx a partial right inverse (PRI) of a given Lévy process X if XKx = x for at least all x in some random interval [0, ζ) of positive length. In this paper, we give a necessary and sufficient condition for the existence of a PRI in terms of the Lévy triplet. © Institute of Mathematical Statistics, 2010.

KW - Creeping

KW - Excursions

KW - Ladder height subordinator

KW - Lévy process

KW - Sample path behavior

U2 - 10.1214/09-AOP515

DO - 10.1214/09-AOP515

M3 - Article

VL - 38

SP - 1390

EP - 1400

JO - Annals of Probability

JF - Annals of Probability

IS - 4

ER -

Right inverses of lévy processes

Abstract

Keywords

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