Probabilistic approach to finding the asymptotic behavior of the solution of nonlinear difference equations

We examine a result which is a transfer of a result due to Kolmogorov, Petrovsky and Piskunov about the limit speed of the wave for the diffusion equation to difference equations. We use a method of M. I. Freidlin in the following way. We derive a formula relating a solution of the equation to a stohastic process. Then the estimation is carried out using the limit properties of the process.