On the backward Euler approximation of the stochastic Allen-Cahn equation
Artikel i vetenskaplig tidskrift, 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.

Allen-Cahn equation

pathwise convergence

Wiener process

Euler method

additive noise

factorization method

Stochastic partial differential equation

strong convergence

Författare

Mihaly Kovacs

University of Otago

Stig Larsson

Chalmers, Matematiska vetenskaper, Matematik

Göteborgs universitet

Fredrik Lindgren

Chalmers, Matematiska vetenskaper, Matematik

Göteborgs universitet

Journal of Applied Probability

0021-9002 (ISSN)

Vol. 52 323-338

Ämneskategorier

Beräkningsmatematik

Fundament

Grundläggande vetenskaper

DOI

10.1239/jap/1437658601