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

被引：22

作者：

Millet, A

Morien, PL

机构：

[1] Univ Paris 06, Probabil Lab, CNRS UMR 7599, F-75252 Paris, France

[2] Univ Paris 10, MODAL X, F-92001 Nanterre, France

来源：

STOCHASTIC PROCESSES AND THEIR APPLICATIONS | 2000年 / 86卷 / 01期

关键词：

stochastic partial differential equation; wave equation; Gaussian noise; Malliavin calculus;

D O I：

10.1016/S0304-4149(99)00090-3

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

We pursue the investigation started in a recent paper by Millet and Sanz-Sole (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 Holder-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 Sec. 5(2), 275-298) based on the Malliavin calculus. (C) 2000 Elsevier Science B.V. All rights reserved.

引用

页码：141 / 162

页数：22

共 10 条

[1] Malliavin calculus for white noise driven parabolic SPDEs [J].