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Weak convergence of Galerkin approximations of stochastic partial differential equations driven by additive Lévy noise

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  • Barth, Andrea
  • Stüwe, Tobias

Abstract

This work considers weak approximations of stochastic partial differential equations (SPDEs) driven by Lévy noise. The SPDEs at hand are parabolic with additive noise processes. A weak-convergence rate for the corresponding Galerkin Finite Element approximation is derived. The convergence result is derived by use of the Malliavin derivative rather than the common approach via the Kolmogorov backward equation.

Suggested Citation

  • Barth, Andrea & Stüwe, Tobias, 2018. "Weak convergence of Galerkin approximations of stochastic partial differential equations driven by additive Lévy noise," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 143(C), pages 215-225.
    • Handle: RePEc:eee:matcom:v:143:y:2018:i:c:p:215-225
    DOI: 10.1016/j.matcom.2017.03.007
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    References listed on IDEAS

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    1. Barth, Andrea & Lang, Annika, 2013. "Lp and almost sure convergence of a Milstein scheme for stochastic partial differential equations," Stochastic Processes and their Applications, Elsevier, vol. 123(5), pages 1563-1587.
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    Cited by:

    1. Yang, Xu & Zhao, Weidong, 2018. "Finite element methods and their error analysis for SPDEs driven by Gaussian and non-Gaussian noises," Applied Mathematics and Computation, Elsevier, vol. 332(C), pages 58-75.

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