On the discretization in time of the stochastic Allen-Cahn equation
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 semidiscretisation in time of the equation by an Euler type split step method. We show that the method converges strongly with a rate O(Δt^γ) for any γ<12. By means of a perturbation argument, we also establish the strong convergence of the standard backward Euler scheme with the same rate.
addi- tive noise
Stochastic partial differential equation