A Markov jump process approximation of the stochastic Burgers equation

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