A Markov jump process approximation of the stochastic Burgers equation

Abstract

We consider the stochastic Burgers equation $ \dnachd{t} ψ(t,r) = Δψ(t,r) + \nabla ψ^2(t,r)+\sqrt{γψ(t,r)} η(t,r) $ with periodic boundary conditions, where $t \ge 0,$ $r \in [0,1],$ and $η$ is some space-time white noise. A certain Markov jump process is constructed to approximate a solution of this equation.}