Gaussian limiting behavior of the rescaled solution to the linear Korteweg-de Vries equation with random initial conditions

Authors
Beghin, L Knopova, VP Leonenko, NN Orsingher, E
Citation
L. Beghin et al., Gaussian limiting behavior of the rescaled solution to the linear Korteweg-de Vries equation with random initial conditions, J STAT PHYS, 99(3-4), 2000, pp. 769-781
Citations number
27
Categorie Soggetti
Physics
Journal title
JOURNAL OF STATISTICAL PHYSICS
ISSN journal
00224715 → ACNP
Volume
99
Issue
3-4
Year of publication
2000
Pages
769 - 781
Database
ISI
SICI code
0022-4715(200005)99:3-4<769:GLBOTR>2.0.ZU;2-0
Abstract
We analyze the asymptotic behavior of the rescaled solution to the linear K orteweg-de Vries equation when the initial conditions are supposed to be ra ndom and weakly dependent. By means of the method of moments we prove the G aussianity of the limiting process and we present its correlation function. The same technique is applied to the analysis of another third-order heat- type equation.