Gaussian scenario for the heat equation with quadratic potential and weakly dependent data with applications

Leonenko, Nikolai N. ORCID: https://orcid.org/0000-0003-1932-4091 and Ruiz-Medina, M. D. 2008. Gaussian scenario for the heat equation with quadratic potential and weakly dependent data with applications. Methodology and Computing in Applied Probability 10 (4) , pp. 595-620. 10.1007/s11009-007-9069-8

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Abstract

For a suitable scaling of the solution to the one-dimensional heat equation with spatial-dependent coefficients and weakly dependent random initial conditions, the convergence to the Gaussian limiting distribution is proved. The scaling proposed and methodology followed allow us to obtain Gaussian scenarios for related equations such as the one-dimensional Burgers equation as well as for the multidimensional formulation of both the heat and Burgers equations. Furthermore, the investigation of non-Gaussian scenarios is opened with a different proposed scaling, proving the convergence of the second-order moments.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Mathematics
Subjects:	Q Science > QA Mathematics
Uncontrolled Keywords:	Burgers equation ; heat equation ; quadratic potentials ; scaling laws ; spatiotemporal random fields ; weak-dependent random initial conditions.
ISSN:	1387-5841
Last Modified:	18 Oct 2022 13:27
URI:	https://orca.cardiff.ac.uk/id/eprint/13956

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