DOI: 10.1007/s10955-005-5960-2 Journal of Statistical Physics, Vol. 120, Nos. 3/4, August 2005 (© 2005) On Travelling Waves for the Stochastic Fisher–Kolmogorov–Petrovsky–Piscunov Equation Joseph G. Conlon 1 and Charles R. Doering 1 Received November 26, 2004; accepted May 4, 2005 This paper is concerned with properties of the wave speed for the stochas- tically perturbed Fisher–Kolmogorov–Petrovsky–Piscunov (FKPP) equation. It was shown in the classical 1937 paper by Kolmogorov, Petrovsky and Piscu- nov that the large time behavior of the solution to the FKPP equation with Heaviside initial data is a travelling wave. In a seminal 1995 paper Mueller and Sowers proved that this also holds for a stochastically perturbed FKPP equa- tion. The wave speed depends on the strength σ of the noise. In this paper bounds on the asymptotic behavior of the wave speed c(σ) as σ → 0 and σ → ∞ are obtained. KEY WORDS: Stochastic pde; contact process; particle systems. 1. INTRODUCTION In this paper we shall be interested in travelling wave solutions to the sto- chastically perturbed Kolmogorov–Petrovsky–Piscounov (FKPP) equation. The FKPP equation, (8,10) u t = u xx + u[1 - u], x ∈ R, t> 0 (1.1) is perhaps the simplest equation which has travelling wave solutions. In fact (1.1) has a solution u(x,t) = f c (x - ct) for any c  2, where the func- tion f c (z) converges exponentially to 1 as z → -∞ and to 0 as z → +∞. In their classic 1937 paper (10) Kolmogorov et al. proved that if u(x,t) is 1 Department of Mathematics and Michigan Center for Theoretical Physics University of Michigan, Ann Arbor, MI 48109-1109; e-mail: conlon@umich.edu, doering@umich.edu 421 0022-4715/05/0800-0421/0 © 2005 Springer Science+Business Media, Inc.