Summary: The stochastic Fisher-Kolmogorov-Petrovsky-Piskunov equation is
for where is a Gaussian white noise process in space and time. Here , and are parameters and the equation is interpreted as the continuum limit of a spatially discretized set of Itô equations. Solutions of this stochastic partial differential equation have an exact connection to the reaction-diffusion system at appropriate values of the rate coefficients and particles’ diffusion constant. This relationship is called “duality” by the probabilists; it is not via some hydrodynamic description of the interacting particle system. In this paper we present a complete derivation of the duality relationship and use it to deduce some properties of solutions to the stochastic Fisher-Kolmogorov-Petrovsky-Piskunov equation.