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Rate of Convergence of Space Time Approximations for Stochastic Evolution Equations

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Abstract

Stochastic evolution equations in Banach spaces with unbounded nonlinear drift and diffusion operators driven by a finite dimensional Brownian motion are considered. Under some regularity condition assumed for the solution, the rates of convergence of various numerical approximations are estimated under strong monotonicity and Lipschitz conditions. The abstract setting involves general consistency conditions and is then applied to a class of quasilinear stochastic PDEs of parabolic type.

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Correspondence to Annie Millet.

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This paper was written while the first named author was visiting the University of Paris 1.

The research of this author is partially supported by EU Network HARP.

The research of the second named author is partially supported by the research project BMF2003-01345.

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Gyöngy, I., Millet, A. Rate of Convergence of Space Time Approximations for Stochastic Evolution Equations. Potential Anal 30, 29–64 (2009). https://doi.org/10.1007/s11118-008-9105-5

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  • DOI: https://doi.org/10.1007/s11118-008-9105-5

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