Potential Analysis

, 31:375 | Cite as

Pathwise Numerical Approximations of SPDEs with Additive Noise under Non-global Lipschitz Coefficients

Article

Abstract

We consider the pathwise numerical approximation of nonlinear parabolic stochastic partial differential equations (SPDEs) driven by additive white noise under local assumptions on the coefficients only. We avoid the standard global Lipschitz assumption in the literature on the coefficients by first showing convergence under global Lipschitz coefficients but with a strong error criteria and then by applying a localization technique for one sample path on a bounded set.

Keywords

Parabolic stochastic partial differential equation Higher order approximation Strong error criteria Global Lipschitz Pathwise approximation 

Mathematics Subject Classifications (2000)

60H15 65C30 35K90 

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Copyright information

© Springer Science+Business Media B.V. 2009

Authors and Affiliations

  1. 1.Institute of MathematicsJohann Wolfgang Goethe-UniversityFrankfurt am MainGermany

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