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

Millet, Annie; Sanz-Solé, Marta

Bernoulli, Tome 6 (2000) no. 6, p. 887-915 / Harvested from Project Euclid

Résumé

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 L^p-norm for p≥1 is also proved.

Publié le : 2000-10-14
Classification: approximations, stochastic partial differential equations, support theorem

@article{1081282694,
     author = {Millet, Annie and Sanz-Sol\'e, Marta},
     title = {Approximation and support theorem for a wave equation in two space dimensions},
     journal = {Bernoulli},
     volume = {6},
     number = {6},
     year = {2000},
     pages = { 887-915},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1081282694}
}

Millet, Annie; Sanz-Solé, Marta. Approximation and support theorem for a wave equation in two space dimensions. Bernoulli, Tome 6 (2000) no. 6, pp.  887-915. http://gdmltest.u-ga.fr/item/1081282694/