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

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.

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Acknowledgements

This project has been partially supported through the SNSF-Research project 200021_156603 “Numerical approximations of nonlinear stochastic ordinary and partial differential equations”.

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Correspondence to Arnulf Jentzen.

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Jentzen, A., Lindner, F. & Pušnik, P. Exponential moment bounds and strong convergence rates for tamed-truncated numerical approximations of stochastic convolutions. Numer Algor 85, 1447–1473 (2020). https://doi.org/10.1007/s11075-019-00871-y

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Keywords

  • Stochastic partial differential equation
  • SPDE
  • Stochastic convolution
  • Tamed-truncated numerical approximation
  • Exponential moment bound
  • Strong convergence rate