Malliavin regularity and weak approximation of semilinear SPDEs with Lévy noise

Adam Andersson; Felix Lindner

doi:10.3934/dcdsb.2019081

Article Contents

2019, Volume 24, Issue 8: 4271-4294. Doi: 10.3934/dcdsb.2019081

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Malliavin regularity and weak approximation of semilinear SPDEs with Lévy noise

Adam Andersson^1, and
Felix Lindner^2, ,

1.
Smarter AI Sweden, Vallgatan 3, SE-411-16 Gothenburg, Sweden
2.
Institute of Mathematics, University of Kassel, Heinrich-Plett-Str. 40, 34132 Kassel, Germany

^* Corresponding author: Felix Lindner
^* Corresponding author: Felix Lindner

Received: June 2018

Revised: November 2018

Early access: April 2019

Published: August 2019

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Abstract

We investigate the weak order of convergence for space-time discrete approximations of semilinear parabolic stochastic evolution equations driven by additive square-integrable Lévy noise. To this end, the Malliavin regularity of the solution is analyzed and recent results on refined Malliavin-Sobolev spaces from the Gaussian setting are extended to a Poissonian setting. For a class of path-dependent test functions, we obtain that the weak rate of convergence is twice the strong rate.

Keywords:

Malliavin calculus,
Poisson random measure,
Lévy process,
stochastic partial differential equation,
numerical approximation,
weak convergence.

Mathematics Subject Classification: Primary: 60H15, 60G51, 60H07; Secondary: 65C30, 65M60.

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