Super-convergence analysis on exponential integrator for stochastic heat equation driven by additive fractional Brownian motion
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In this paper, we consider the strong convergence order of the exponential integrator for the stochastic heat equation driven by an additive fractional Brownian motion with Hurst parameter H∈(1/2,1). By showing the strong order one of accuracy of the exponential integrator under appropriote assumptions, we present the first super-convergence result in temporal direction on full discretizations for stochastic partial differential equations driven by infinite dimensional fractional Brownian motions with Hurst parameter H∈(1/2,1). The proof is a combination of Malliavin calculus, the L^p(Ω)-estimate of the Skorohod integral and the smoothing effect of the Laplacian operator.
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