Gaussian density estimates for solutions to quasi-linear stochastic partial differential equations |
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Authors: | David Nualart Lluís Quer-Sardanyons |
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Institution: | aDepartment of Mathematics, University of Kansas, Lawrence, Kansas, 66045, USA;bDepartament de Matemàtiques, Universitat Autònoma de Barcelona, 08193 Bellaterra, Barcelona, Spain |
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Abstract: | In this paper we establish lower and upper Gaussian bounds for the solutions to the heat and wave equations driven by an additive Gaussian noise, using the techniques of Malliavin calculus and recent density estimates obtained by Nourdin and Viens in 17]. In particular, we deal with the one-dimensional stochastic heat equation in 0, 1] driven by the space-time white noise, and the stochastic heat and wave equations in Rd (d≥1 and d≤3, respectively) driven by a Gaussian noise which is white in time and has a general spatially homogeneous correlation. |
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Keywords: | Gaussian bounds Malliavin calculus Spatially homogeneous Gaussian noise Stochastic partial differential equations |
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