Fractional stochastic Burgers-type equation in Holder space-Wellposedness and approximations

摘要

In this work, we use the spectral Galerkin method to prove the existence of a pathwise unique mild solution of a fractional stochastic partial differential equation of Burgers type in a Holder space. We get the temporal regularity, and using a combination of Galerkin and exponential-Euler methods, we obtain a full discretization scheme of the solution. Moreover, we calculate the rates of convergence for both approximations (Galerkin and full discretization) with respect to time and to space.