## 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

#### 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 *L*^{p}-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