Extensions of regularity for a lÉvy process∗

R. A. Maller

doi:10.1137/S0040585X97T988824

Extensions of regularity for a lÉvy process^∗

R. A. Maller^*

^*Corresponding author for this work

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

Abstract

We obtain necessary and sufficient conditions for the finiteness of certain moment functions of the random variable T₀ ⁻, which is the first passage time of a Lévy process (X_t)_t≥₀ below zero, and the position X_{T −} of the process at this time. Our results generalize classical results of Rogozin and Bertoin on the⁰ regularity of X, and extend earlier results of Blumenthal and Getoor on the regularity index.

Original language	English
Pages (from-to)	575-603
Number of pages	29
Journal	Theory of Probability and its Applications
Volume	62
Issue number	4
DOIs	https://doi.org/10.1137/S0040585X97T988824
Publication status	Published - 2018

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title = "Extensions of regularity for a l{\'E}vy process∗ ",

abstract = "We obtain necessary and sufficient conditions for the finiteness of certain moment functions of the random variable T0 −, which is the first passage time of a L{\'e}vy process (Xt)t≥0 below zero, and the position XT − of the process at this time. Our results generalize classical results of Rogozin and Bertoin on the0 regularity of X, and extend earlier results of Blumenthal and Getoor on the regularity index.",

keywords = "Dominance of the positive part of a l{\'e}vy process over the negative part, Dominated variation conditions, First passage of a l{\'e}vy process below zero, First passage time, Regularity of a real-valued l{\'e}vy process, Rogozin regularity condition",

author = "Maller, {R. A.}",

note = "Publisher Copyright: {\textcopyright} 2018 Society for Industrial and Applied Mathematics and by SIAM.",

year = "2018",

doi = "10.1137/S0040585X97T988824",

language = "English",

volume = "62",

pages = "575--603",

journal = "Theory of Probability and its Applications",

issn = "0040-585X",

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TY - JOUR

T1 - Extensions of regularity for a lÉvy process∗

AU - Maller, R. A.

PY - 2018

Y1 - 2018

N2 - We obtain necessary and sufficient conditions for the finiteness of certain moment functions of the random variable T0 −, which is the first passage time of a Lévy process (Xt)t≥0 below zero, and the position XT − of the process at this time. Our results generalize classical results of Rogozin and Bertoin on the0 regularity of X, and extend earlier results of Blumenthal and Getoor on the regularity index.

AB - We obtain necessary and sufficient conditions for the finiteness of certain moment functions of the random variable T0 −, which is the first passage time of a Lévy process (Xt)t≥0 below zero, and the position XT − of the process at this time. Our results generalize classical results of Rogozin and Bertoin on the0 regularity of X, and extend earlier results of Blumenthal and Getoor on the regularity index.

KW - Dominance of the positive part of a lévy process over the negative part

KW - Dominated variation conditions

KW - First passage of a lévy process below zero

KW - First passage time

KW - Regularity of a real-valued lévy process

KW - Rogozin regularity condition

UR - http://www.scopus.com/inward/record.url?scp=85055149839&partnerID=8YFLogxK

U2 - 10.1137/S0040585X97T988824

DO - 10.1137/S0040585X97T988824

M3 - Article

SN - 0040-585X

VL - 62

SP - 575

EP - 603

JO - Theory of Probability and its Applications

JF - Theory of Probability and its Applications

IS - 4

ER -

Extensions of regularity for a lÉvy process^∗

Abstract

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