We prove a maximum principle for local solutions of quasi-linear parabolic stochastic PDEs, with non-homogeneous second order operator on a bounded domain and driven by a space–time white noise. Our method based on an approximation of the domain and the coefficients of the operator, does not...

The stochastic Fisher–Kolmogorov–Petrovsky–Piscunov equation is∂tU(x,t)=D∂xxU+γU(1−U)+εU(1−U)η(x,t)for 0⩽U⩽1 where η(x,t) is a Gaussian white noise process in space and time. Here D, γ and ε are parameters and the equation is interpreted as the continuum limit of a...