Pathwise Numerical Approximations of SPDEs with Additive Noise under Non-global Lipschitz Coefficients
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- Jentzen, A. Potential Anal (2009) 31: 375. doi:10.1007/s11118-009-9139-3
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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.