dc.contributor
Centre de Recerca Matemàtica
dc.contributor.author
Nualart Dexeus, Eulàlia
dc.contributor.author
Quer-Sardanyons, Lluís
dc.date.accessioned
2011-07-13T08:42:19Z
dc.date.accessioned
2024-09-19T13:33:49Z
dc.date.available
2011-07-13T08:42:19Z
dc.date.available
2024-09-19T13:33:49Z
dc.identifier.uri
http://hdl.handle.net/2072/152167
dc.description.abstract
In this paper, we establish lower and upper Gaussian bounds for the probability density of the mild solution to the stochastic heat equation with multiplicative noise and in any space dimension. The driving perturbation is a Gaussian noise which is white in time with some spatially homogeneous covariance. These estimates are obtained using tools of the Malliavin calculus. The most challenging part is the lower bound, which is obtained by adapting a general method developed by Kohatsu-Higa to the underlying spatially homogeneous Gaussian setting. Both lower and upper estimates have the same form: a Gaussian density with a variance which is equal to that of the mild solution of the corresponding linear equation with additive noise.
cat
dc.format.extent
336693 bytes
dc.format.mimetype
application/pdf
dc.publisher
Centre de Recerca Matemàtica
ca
dc.relation.ispartofseries
Prepublicacions del Centre de Recerca Matemàtica;968
dc.rights
Aquest document està subjecte a una llicència d'ús de Creative Commons, amb la qual es permet copiar, distribuir i comunicar públicament l'obra sempre que se'n citin l'autor original, la universitat i el centre i no se'n faci cap ús comercial ni obra derivada, tal com queda estipulat en la llicència d'ús (http://creativecommons.org/licenses/by-nc-nd/2.5/es/)
cat
dc.subject.other
Malliavin, Càlcul de
ca
dc.subject.other
Equacions estocàstiques diferencials
ca
dc.title
Gaussian estimates for the density of the non-linear stochastic heat equation in any space dimension
ca
dc.type
info:eu-repo/semantics/preprint
ca
