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

Donatas Surgailis

Stochastic Processes and their Applications, 2024, vol. 174, issue C

Abstract: We study scaling limits of nonlinear functions G of random grain model X on Rd 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=λγ, 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.

Keywords: Random grain model; Boolean model; Scaling limit; Charlier polynomials; Mehler’s formula; Burgers’ equation (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1016/j.spa.2024.104390

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