Optimal rate of convergence for approximations of nonlinear SPDEs with additive space-time white noise

Abstract

We consider exponential Euler approximations of nonlinear stochastic reaction-diffusion equations driven by a 1+1-dimensional white noise and prove a strong rate of convergence of 1/2 in space and, crucially, 1 in time. This generalizes the results by Jentzen/Kloeden '08 to truly nonlinear coefficients and thus overcomes the previous order barrier. Joint work with Ana Djurdjevac and Máté Gerencsér.