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On a stochastic wave equation in two space dimensions: regularity of the solution and its density

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  • Millet, Annie
  • Morien, Pierre-Luc

Abstract

We pursue the investigation started in a recent paper by Millet and Sanz-Solé (1999, Ann. Probab. 27, 803-844) concerning a non-linear wave equation driven by a Gaussian white noise in time and correlated in the two-dimensional space variable. Under more restrictive conditions on the covariance function of the noise, we prove Hölder-regularity properties for both the solution and its density. For the latter, we adapt the method used in a paper by Morien (1999, Bernoulli: Official J. Bernoulli Soc. 5(2), 275-298) based on the Malliavin calculus.

Suggested Citation

  • Millet, Annie & Morien, Pierre-Luc, 2000. "On a stochastic wave equation in two space dimensions: regularity of the solution and its density," Stochastic Processes and their Applications, Elsevier, vol. 86(1), pages 141-162, March.
    • Handle: RePEc:eee:spapps:v:86:y:2000:i:1:p:141-162
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    Cited by:

    1. Márquez-Carreras, D. & Mellouk, M. & Sarrà, M., 2001. "On stochastic partial differential equations with spatially correlated noise: smoothness of the law," Stochastic Processes and their Applications, Elsevier, vol. 93(2), pages 269-284, June.

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