Open Access
2015 Absolute continuity for SPDEs with irregular fundamental solution
Marta Sanz-Solé, André Süss
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Electron. Commun. Probab. 20: 1-11 (2015). DOI: 10.1214/ECP.v20-3831


For a class of stochastic partial differential equations studied by Conus and Dalang, we prove the existence of density of the probability law of the solution at a given point $(t,x)$, and that the density belongs to some Besov space. The proof relies on a method developed by Debussche and Romito.The result can be applied to the solution of the stochastic wave equation with multiplicative noise, Lipschitz coefficients and any spatial dimension $d\ge 1$, and also to the heat equation.This provides an extension of earlier results.


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Marta Sanz-Solé. André Süss. "Absolute continuity for SPDEs with irregular fundamental solution." Electron. Commun. Probab. 20 1 - 11, 2015.


Accepted: 14 February 2015; Published: 2015
First available in Project Euclid: 7 June 2016

zbMATH: 1321.60138
MathSciNet: MR3314649
Digital Object Identifier: 10.1214/ECP.v20-3831

Primary: 60H07 , 60H15
Secondary: 60H05 , 60H20

Keywords: densities , Stochastic partial differential equations , Stochastic wave equation

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