On the backward Euler approximation of the stochastic Allen-Cahn equation
Journal article, 2015

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(Δt^γ) for any γ < ½. We also prove that the scheme converges uniformly in the strong L^p -sense but with no rate given.

Wiener process

Stochastic partial differential equation

factorization method

additive noise

strong convergence

Allen-Cahn equation

pathwise convergence

Euler method


Mihaly Kovacs

University of Otago

Stig Larsson

Chalmers, Mathematical Sciences, Mathematics

University of Gothenburg

Fredrik Lindgren

University of Gothenburg

Chalmers, Mathematical Sciences, Mathematics

Journal of Applied Probability

0021-9002 (ISSN)

Vol. 52 2 323-338

Subject Categories

Computational Mathematics


Basic sciences



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