Gaussian density estimates for solutions to quasi-linear stochastic partial differential equations

David Nualart and Lluís Quer-Sardanyons

Stochastic Processes and their Applications, 2009, vol. 119, issue 11, 3914-3938

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 (d>=1 and d

Keywords: Gaussian; bounds; Malliavin; calculus; Spatially; homogeneous; Gaussian; noise; Stochastic; partial; differential; equations (search for similar items in EconPapers)
Date: 2009
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Citations: View citations in EconPapers (2)

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