Fractional stochastic Burgers‐type equation in Hölder space—Wellposedness and approximations

Abstract

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 Hölder 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.

Temporal regularity of stochastic differential equations driven by G-Brownian motion

“…Stochastic (partial) differential equations play a prominent role in modelling many phenomena in applied sciences. There is a huge number of works in the literature that are concerned with this type of equations, see for a short list [1,2,3,4,5].…”