Effect of stochastic perturbations for front propagation in Kolmogorov Petrovskii Piscunov equations

In the second situation (noise with spatial covariance which decays to 0 at ±∞, stochastic integral taken in the sense of Itô), a travelling front can be defined for all ϵ>0. Its average asymptotic speed does not depend on ϵ and is the classical wave speed of the unperturbed KPP equation.