A stochastic wave equation in two space dimension:: Smoothness of the law
成果类型：
Article
署名作者：
Millet, A; Sanz-Solé, M
署名单位：
Sorbonne Universite; University of Barcelona; Universite Paris Nanterre
刊物名称：
ANNALS OF PROBABILITY
ISSN/ISSBN：
0091-1798
DOI：
10.1214/aop/1022677387
发表日期：
1999
页码：
803-844
关键词：
摘要：
We prove the existence and uniqueness, for any time, of a real-valued process solving a nonlinear stochastic wave equation driven by a Gaussian noise white in time and correlated in the two-dimensional space variable. We prove that the solution is regular in the sense of the Malliavin calculus. We also give a decay condition on the covariance function of the noise under which the solution has Holder continuous trajectories and show that, under an additional ellipticity assumption, the law of the solution at any strictly positive time has a smooth density.