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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.

MSC:

65C30 Numerical solutions to stochastic differential and integral equations
60H15 Stochastic partial differential equations (aspects of stochastic analysis)
35R60 PDEs with randomness, stochastic partial differential equations
35K58 Semilinear parabolic equations
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
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