Scaling Limits of Solutions of SPDE Driven by L\'evy White Noises

Julien Fageot; Michael Unser

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arXiv · 1610.06711

Scaling Limits of Solutions of SPDE Driven by L\'evy White Noises

Julien Fageot·Michael Unser

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Abstract

Consider a random process s solution of the stochastic partial differential equation Ls = w with L a homogeneous operator and w a multidimensional L\'evy white noise. In this paper, we study the asymptotic effect of zooming in or zooming out of the process s. More precisely, we give sufficient conditions on L and w so that the rescaled versions of s converges in law to a self-similar process of order H at coarse scales and at fine scales. The parameter H depends on the homogeneity order of the operator L and the Blumenthal-Getoor indices associated to the L\'evy white noise w. Finally, we apply our general results to several notorious classes of random processes and random fields.

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Julien Fageot, Michael Unser. 2016-10-21. Scaling Limits of Solutions of SPDE Driven by L\'evy White Noises. https://arxiv.org/abs/1610.06711

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