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Smoothness of the functional law generated by a nonlinear SPDE

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Abstract

The authors consider a stochastic heat equation in dimension d = 1 driven by an additive space time white noise and having a mild nonlinearity. It is proved that the functional law of its solution is absolutely continuous and possesses a smooth density with respect to the functional law of the corresponding linear SPDE.

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Authors and Affiliations

  1. Facultat de Matemàtiques, Universitat de Barcelona, Gran Via 585, E-08007, Barcelona, Spain

    Marta Sanz-Solé

  2. 10, rue Saint Louis-en-l’Ile, F-74004, Paris, France

    Paul Malliavin

Authors
  1. Marta Sanz-Solé
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  2. Paul Malliavin
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Corresponding author

Correspondence to Marta Sanz-Solé.

Additional information

Project supported by the grant MTM 2006-01351 from the Dirección General de Investigación, Ministerio de Educación y Ciencia, Spain.

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Sanz-Solé, M., Malliavin, P. Smoothness of the functional law generated by a nonlinear SPDE. Chin. Ann. Math. Ser. B 29, 113–120 (2008). https://doi.org/10.1007/s11401-007-0508-1

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  • DOI: https://doi.org/10.1007/s11401-007-0508-1

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