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

2022/12/23 by Surgailis, Donatas
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2212.12203

Abstract

We study scaling limits of nonlinear functions G of random grain model X on ℝ^d with long-range 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 λ as M = λ^γ, for some γ> 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.

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