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Exponential moment bounds and strong convergence rates for tamed-truncated numerical approximations of stochastic convolutions

by A. Jentzen and F. Lindner and P. Pušnik

(Report number 2019-02)

Abstract
In this article we establish exponential moment bounds, moment bounds in fractional order smoothness spaces, a uniform Hölder continuity in time, and strong convergence rates for a class of fully discrete exponential Euler-type numerical approximations of infinite dimensional stochastic convolution processes. The considered approximations involve specific taming and truncation terms and are therefore well suited to be used in the context of SPDEs with non-globally Lipschitz continuous nonlinearities.

Keywords:

@Techreport{JLP19_806,
  author = {A. Jentzen and F. Lindner and P. Pušnik},
  title = {Exponential moment bounds and strong convergence rates for tamed-truncated numerical  approximations of stochastic convolutions},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2019-02},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2019/2019-02.pdf },
  year = {2019}
}

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