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

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  • Surgailis, Donatas

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.

Suggested Citation

  • Surgailis, Donatas, 2024. "Scaling limits of nonlinear functions of random grain model, with application to Burgers’ equation," Stochastic Processes and their Applications, Elsevier, vol. 174(C).
    • Handle: RePEc:eee:spapps:v:174:y:2024:i:c:s0304414924000966
    DOI: 10.1016/j.spa.2024.104390
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