A numerical scheme for stochastic PDEs with Gevrey regularity

We consider strong approximations to parabolic stochastic PDEs. We assume the noise lies in a Gevrey space of analytic functions. This type of stochastic forcing includes the case of forcing in a finite number of Fourier modes. We show that with Gevrey noise our numerical scheme has solutions in a discrete equivalent of this space and prove a strong error estimate. Finally we present some numerical results for a stochastic PDE with a Ginzburg–Landau nonlinearity and compare this to the more standard implicit Euler–Maruyama scheme.