Macroscaling limit theorems for filtered spatiotemporal random fields

Anh, V. V., Leonenko, Nikolai N. ORCID: https://orcid.org/0000-0003-1932-4091 and Ruiz-Medina, M. D. 2013. Macroscaling limit theorems for filtered spatiotemporal random fields. Stochastic Analysis and Applications 31 (3) , pp. 460-508. 10.1080/07362994.2013.777280

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Abstract

This article addresses the problem of defining a general scaling setting in which Gaussian and non-Gaussian limit distributions of linear random fields can be obtained. The linear random fields considered are defined by the convolution of a Green kernel, satisfying suitable scaling conditions, with a non-linear transformation of a Gaussian centered homogeneous random field. The results derived cover the weak-dependence and strong-dependence cases for such Gaussian random fields. Extension to more general random initial conditions defined, for example, in terms of non-linear transformations of χ2-random fields, is also discussed. For an example, we consider the random fractional diffusion equation. The vectorial version of the limit theorems derived is also formulated, including the limit distribution of the parabolically rescaled solution to the Burgers equation in the cases of weakly and strongly dependent initial potentials.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Mathematics
Subjects:	Q Science > QA Mathematics
Uncontrolled Keywords:	Burgers equation, Central limit theorem, Filtered linear random fields, Fractional (in time and/or in space) diffusion equations, Random partial differential equations, Random fractional partial differential equations, Non-central limit theorem
Publisher:	Taylor and Francis
ISSN:	0736-2994
Last Modified:	24 Oct 2022 11:03
URI:	https://orca.cardiff.ac.uk/id/eprint/46751

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