Bernoulli

  • Bernoulli
  • Volume 6, Number 5 (2000), 887-915.

Approximation and support theorem for a wave equation in two space dimensions

Annie Millet and Marta Sanz-Solé

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Abstract

We prove a characterization of the support of the law of the solution for a stochastic wave equation with two-dimensional space variable, driven by a noise white in time and correlated in space. The result is a consequence of an approximation theorem, in the convergence of probability, for equations obtained by smoothing the random noise. For some particular classes of coefficients, approximation in the Lp-norm for p≥1 is also proved.

Article information

Source
Bernoulli, Volume 6, Number 5 (2000), 887-915.

Dates
First available in Project Euclid: 6 April 2004

Permanent link to this document
https://projecteuclid.org/euclid.bj/1081282694

Mathematical Reviews number (MathSciNet)
MR2001m:60147

Zentralblatt MATH identifier
0968.60059

Keywords
approximations stochastic partial differential equations support theorem

Citation

Millet, Annie; Sanz-Solé, Marta. Approximation and support theorem for a wave equation in two space dimensions. Bernoulli 6 (2000), no. 5, 887--915. https://projecteuclid.org/euclid.bj/1081282694


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References

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  • [2] Dalang, R. and Frangos, N. (1998) The stochastic wave equation in two spatial dimensions. Annals of Probab., 26, 187-212.
  • [3] Millet, A. and Sanz-Solé, M. (1994a) The support of an hyperbolic stochastic partial differential equation. Probab. Theory Related Fields, 98, 361-387.
  • [4] Millet, A. and Sanz-Solé, M. (1994b) A simple proof of the support theorem for diffusion processes. In J. Azéma, P.-A. Meyer and M. Yor (eds), Séminaire de Probabilités XXVIII, Lecture Notes in Math. 1583, pp. 36-48. Berlin: Springer-Verlag.
  • [5] Millet, A. and Sanz-Solé, M. (1999) A stochastic wave equation in two space dimensions: Smoothness of the law. Ann. Probab., 27, 803-844.
  • [6] Millet, A. and Morien, P.-L. (2000) On a stochastic wave equation in two space dimensions: regularity of the solution and its density. Stoch. Proc. Appl., 86, 141-162.