Symmetric infinitely divisible processes with sample paths in Orlicz spaces and absolute continuity of infinitely divisible processes

Michael Braverman; Gennady Samorodnitsky

doi:10.1016/S0304-4149(98)00055-6

Symmetric infinitely divisible processes with sample paths in Orlicz spaces and absolute continuity of infinitely divisible processes

Michael Braverman, Gennady Samorodnitsky

Department of Mathematics

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

7 Scopus citations

Abstract

We give necessary and sufficient conditions under which a symmetric measurable infinitely divisible process has sample paths in an Orlicz space L_ψ with a function ψ satisfying the Δ₂ condition and, as an application, obtain necessary and sufficient conditions for a symmetric infinitely divisible process to have a version with absolutely continuous paths.

Original language	English
Pages (from-to)	1-26
Number of pages	26
Journal	Stochastic Processes and their Applications
Volume	78
Issue number	1
DOIs	https://doi.org/10.1016/S0304-4149(98)00055-6
State	Published - 1 Oct 1998

Keywords

60E07
60G17
Absolute continuity
Infinitely divisible processes
Integrability
Lévy measures in Banach spaces
Orlicz spaces* L spaces
Primary 60B11
Random series
Stable processes

ASJC Scopus subject areas

Statistics and Probability
Modeling and Simulation
Applied Mathematics

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10.1016/S0304-4149(98)00055-6

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abstract = "We give necessary and sufficient conditions under which a symmetric measurable infinitely divisible process has sample paths in an Orlicz space Lψ with a function ψ satisfying the Δ2 condition and, as an application, obtain necessary and sufficient conditions for a symmetric infinitely divisible process to have a version with absolutely continuous paths.",

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AU - Samorodnitsky, Gennady

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N2 - We give necessary and sufficient conditions under which a symmetric measurable infinitely divisible process has sample paths in an Orlicz space Lψ with a function ψ satisfying the Δ2 condition and, as an application, obtain necessary and sufficient conditions for a symmetric infinitely divisible process to have a version with absolutely continuous paths.

AB - We give necessary and sufficient conditions under which a symmetric measurable infinitely divisible process has sample paths in an Orlicz space Lψ with a function ψ satisfying the Δ2 condition and, as an application, obtain necessary and sufficient conditions for a symmetric infinitely divisible process to have a version with absolutely continuous paths.

KW - 60E07

KW - 60G17

KW - Absolute continuity

KW - Infinitely divisible processes

KW - Integrability

KW - Lévy measures in Banach spaces

KW - Orlicz spaces L spaces

KW - Primary 60B11

KW - Random series

KW - Stable processes

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JO - Stochastic Processes and their Applications

JF - Stochastic Processes and their Applications

IS - 1

ER -

Symmetric infinitely divisible processes with sample paths in Orlicz spaces and absolute continuity of infinitely divisible processes

Abstract

Keywords

ASJC Scopus subject areas

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