On stochastic partial differential equations with spatially correlated noise: smoothness of the law

D. Márquez-Carreras, M. Mellouk and M. Sarrà

Stochastic Processes and their Applications, 2001, vol. 93, issue 2, 269-284

Abstract: We deal with the following general kind of stochastic partial differential equations:with null initial conditions, L a second-order partial differential operator and F a Gaussian noise, white in time and correlated in space. Firstly, we prove that the solution u(t,x) possesses a smooth density pt,x for every . We use the tools of Malliavin Calculus. Secondly, we apply this general result to two particular cases: the d-dimensional spatial heat equation, d[greater-or-equal, slanted]1, and the wave equation, d[set membership, variant]{1,2}.

Keywords: Stochastic; partial; differential; equation; Wave; and; heat; equation; Gaussian; noise; Malliavin; Calculus (search for similar items in EconPapers)
Date: 2001
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Citations: View citations in EconPapers (3)

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