Fast-Diffusion Limit for Reaction–Diffusion Equations with Degenerate Multiplicative and Additive Noise

In the present work we consider a quite general class of reaction–diffusion equations forced by additive and multiplicative noise. When the diffusion is large, one can approximate the solutions of the stochastic reaction–diffusion equations with polynomial term by the solutions of a stochastic ordinary equations with additive noise. We illustrate our results by applying it to logistic equation and nonlinear heat equation.