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2019 Existence of density for the stochastic wave equation with space-time homogeneous Gaussian noise
Raluca M. Balan, Lluís Quer-Sardanyons, Jian Song
Electron. J. Probab. 24: 1-43 (2019). DOI: 10.1214/19-EJP363

Abstract

In this article, we consider the stochastic wave equation on $\mathbb{R} _{+} \times \mathbb{R} $, driven by a linear multiplicative space-time homogeneous Gaussian noise whose temporal and spatial covariance structures are given by locally integrable functions $\gamma $ (in time) and $f$ (in space), which are the Fourier transforms of tempered measures $\nu $ on $\mathbb{R} $, respectively $\mu $ on $\mathbb{R} $. Our main result shows that the law of the solution $u(t,x)$ of this equation is absolutely continuous with respect to the Lebesgue measure.

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Raluca M. Balan. Lluís Quer-Sardanyons. Jian Song. "Existence of density for the stochastic wave equation with space-time homogeneous Gaussian noise." Electron. J. Probab. 24 1 - 43, 2019. https://doi.org/10.1214/19-EJP363

Information

Received: 17 May 2018; Accepted: 18 September 2019; Published: 2019
First available in Project Euclid: 1 October 2019

zbMATH: 07142900
MathSciNet: MR4017124
Digital Object Identifier: 10.1214/19-EJP363

Subjects:
Primary: 60H07, Primary 60H15

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