Malliavin regularity and weak approximation of semilinear SPDEs with Lévy noise | Zendy

Adam Andersson | Zendy; Felix Lindner | Zendy

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Malliavin regularity and weak approximation of semilinear SPDEs with Lévy noise

Author(s) -

Adam Andersson,

Felix Lindner

Publication year - 2019

Publication title -

discrete and continuous dynamical systems - b

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.864

H-Index - 53

eISSN - 1553-524X

pISSN - 1531-3492

DOI - 10.3934/dcdsb.2019081

Subject(s) - mathematics , sobolev space , square integrable function , rate of convergence , gaussian , weak convergence , malliavin calculus , mathematical analysis , integrable system , convergence (economics) , space (punctuation) , noise (video) , pure mathematics , stochastic partial differential equation , physics , computer science , partial differential equation , computer network , channel (broadcasting) , image (mathematics) , computer security , quantum mechanics , artificial intelligence , economics , asset (computer security) , economic growth , operating system

We investigate the weak order of convergence for space-time discrete approximations of semilinear parabolic stochastic evolution equations driven by additive square-integrable Levy 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.

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