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Title:
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Gaussian estimates for the density of the non-linear stochastic heat equation in any space dimension
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Author:
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Nualart Dexeus, Eulàlia; Quer-Sardanyons, Lluís
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Other authors:
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Centre de Recerca Matemàtica |
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Resum:
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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. |
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Publication date:
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2010-10 |
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Subject (UDC):
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519.1 - Teoria general de l'anàlisi combinatòria. Teoria de grafs |
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Subject(s):
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Malliavin, Càlcul de
Equacions estocàstiques diferencials |
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Rights:
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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/) |
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Document type:
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Preprint |
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