Cardiff University | Prifysgol Caerdydd ORCA
Online Research @ Cardiff 
WelshClear Cookie - decide language by browser settings

Macroscaling limit theorems for filtered spatiotemporal random fields

Anh, V. V., Leonenko, Nikolai N. ORCID: 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

Full text not available from this repository.


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

Citation Data

Cited 11 times in Scopus. View in Scopus. Powered By Scopus® Data

Actions (repository staff only)

Edit Item Edit Item