Scaling limits of nonlinear functions of random grain model, with application to Burgers' equation

We study scaling limits of nonlinear functions G of random grain model X on R-d with longrange dependence and marginal Poisson distribution. Following Kaj et al. (2007) we assume that the intensity M of the underlying Poisson process of grains increases together with the scaling parameter lambda as M = lambda (gamma) , for some gamma > 0 . The results are applicable to the Boolean model and exponential G and rely on an expansion of G in Charlier polynomials and a generalization of Mehler's formula. Application to solution of Burgers' equation with initial aggregated random grain data is discussed.