Abstract
We consider the stochastic Allen-Cahn equation perturbed by smooth additive Gaussian noise in a spatial domain with smooth boundary in dimension d ≤ 3, and study the semidiscretization in time of the equation by an implicit Euler method. We show that the method converges pathwise with a rate O(Δ t γ) for any γ < ½. We also prove that the scheme converges uniformly in the strong L p -sense but with no rate given.
Citation
Mihály Kovács. Stig Larsson. Fredrik Lindgren. "On the backward Euler approximation of the stochastic Allen-Cahn equation." J. Appl. Probab. 52 (2) 323 - 338, June 2015. https://doi.org/10.1239/jap/1437658601
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