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

Annie Millet (1, 2) , Pierre-Luc Morien (2)

1 LPMA - Laboratoire de Probabilités et Modèles Aléatoires
2 MODAL'X - Modélisation aléatoire de Paris X

We pursue the investigation started in a recent paper by Millet and Sanz-Solé 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 based on the Malliavin calculus.

Mots clés: Stochastic partial differential equation; Wave equation; Gaussian noise; Malliavin calculus

Domaines: Probabilités [math.PR]

Annie Millet, Pierre-Luc Morien. On a stochastic wave equation in two space dimension: regularity of the solution and its density. Stochastic Processes and their Applications, 2000, 86 (1), pp.141-162. ⟨10.1016/S0304-4149(99)00090-3⟩. ⟨hal-00258033⟩