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Higher order pathwise numerical approximations of SPDEs with additive noise. (English) Zbl 1228.65015
The author considers the numerical approximation of semilinear parabolic stochastic partial differential equations (SPDEs) with additive noise in the form $$dX_{t}=[AX_{t}+F(X_{t})]dt+BdW_{t}.$$ In the equation, $X_{t}\ $ belongs to a Hilbert space $H,\ W_{t}$ is a Wiener process on a Hilbert space $U,\ A$ is an unbounded linear operator, $B$ is a bounded linear operator, $F$ is a nonlinear operator. The main result of the article shows that pathwise convergence of the method proposed by the author has a higher order convergence rate than the Euler scheme.

65C30Stochastic differential and integral equations
60H15Stochastic partial differential equations
35R60PDEs with randomness, stochastic PDE
35K58Semilinear parabolic equations
65M12Stability and convergence of numerical methods (IVP of PDE)
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