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Strong convergence rates for an explicit numerical approximation method for stochastic evolution equations with non-globally Lipschitz continuous nonlinearities

by A. Jentzen and P. Pusnik

(Report number 2015-10)

Abstract
In this article we propose a new, explicit and easily implementable numerical method for approximating a class of semilinear stochastic evolution equations with non-globally Lipschitz continuous nonlinearities. We establish strong convergence rates for this approximation method in the case of semilinear stochastic evolution equations with globally monotone coefficients. Our strong convergence result, in particular, applies to a class of stochastic reaction-diffusion partial differential equations.

Keywords: Numerical approximation, stochastic differential equation, tamed numerical scheme, strong convergence rate, bootstrap argument, temporal approximation, spectral Galerkin method

@Techreport{JP15_600,
  author = {A. Jentzen and P. Pusnik},
  title = {Strong convergence rates for an explicit numerical 
approximation method for stochastic evolution equations with 
non-globally Lipschitz continuous nonlinearities},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2015-10},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2015/2015-10.pdf },
  year = {2015}
}

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