Peierls-Boltzmann equation for ballistic deposition

We consider nonlinear stochastic field equations. Going over to a Fokker-Planck description, we construct a self-consistent expansion around a model evolution equation. In second order the equation for the two-paint function resembles the Peierls-Boltzmann equation for the average number of phonons, but involves also the unknown characteristic frequency function. Within the same expansion we obtain an equation for that function too. The two coupled equations are studied specifically for the case of ballistic deposition. We show how to obtain the exact asymptotic solution of the two coupled nonlinear integral equations obtained in second order. Higher orders are also discussed.