Regularisation of cylindrical L\'evy processes in Besov spaces

Matthew Griffiths; Markus Riedle

Regularisation of cylindrical L\'evy processes in Besov spaces

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Abstract

In this work, we quantify the irregularity of a given cylindrical Lévy process L in $L^2(\R^d)$ by determining the range of weighted Besov spaces B in which L has a regularised version Y, that is a stochastic process Y in the classical sense with values in B. Our approach is based on characterising Lévy measures on Besov spaces. As a by-product, we determine those Besov spaces B for which the embedding of $L^2(\R^d)$ into B is 0-Radonifying and p-Radonifying for p>1.

Original language	English
Journal	Studia Mathematica
Publication status	Accepted/In press - 3 Sept 2024

Keywords

cylindrical processes
generalised processes
Radonifying operators
regularisation
Besov spaces

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BesovMembershipAccepted author manuscript, 496 KBLicence: CC BY

Cite this

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title = "Regularisation of cylindrical L\'evy processes in Besov spaces",

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AU - Griffiths, Matthew

AU - Riedle, Markus

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N2 - In this work, we quantify the irregularity of a given cylindrical Lévy process L in $L^2(\R^d)$ by determining the range of weighted Besov spaces B in which L has a regularised version Y, that is a stochastic process Y in the classical sense with values in B. Our approach is based on characterising Lévy measures on Besov spaces. As a by-product, we determine those Besov spaces B for which the embedding of $L^2(\R^d)$ into B is 0-Radonifying and p-Radonifying for p>1.

AB - In this work, we quantify the irregularity of a given cylindrical Lévy process L in $L^2(\R^d)$ by determining the range of weighted Besov spaces B in which L has a regularised version Y, that is a stochastic process Y in the classical sense with values in B. Our approach is based on characterising Lévy measures on Besov spaces. As a by-product, we determine those Besov spaces B for which the embedding of $L^2(\R^d)$ into B is 0-Radonifying and p-Radonifying for p>1.

KW - cylindrical processes

KW - generalised processes

KW - Radonifying operators

KW - regularisation

KW - Besov spaces

M3 - Article

SN - 0039-3223

JO - Studia Mathematica

JF - Studia Mathematica

ER -

Regularisation of cylindrical L\'evy processes in Besov spaces

Abstract

Keywords

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