Optimal rate of convergence for approximations of SPDEs with non-regular drift

Abstract

A fully discrete finite difference scheme for stochastic reaction-diffusion equations driven by a $1+1$-dimensional white noise is studied. The optimal strong rate of convergence is proved without posing any regularity assumption on the non-linear reaction term. The proof relies on stochastic sewing techniques.

35 pages

References in corpus (2)

• Quantifying a convergence theorem of Gyöngy and Krylov
• Mild Stochastic Sewing Lemma, SPDE in Random Environment, and Fractional Averaging

Cited by in corpus (1)

• Strong convergence of parabolic rate $1$ of discretisations of stochastic Allen-Cahn-type equations