Existence of density for the stochastic wave equation with space-time homogeneous gaussian noise

Raluca M. Balan, Lluís Quer-Sardanyons, Jian Song

Research output: Contribution to journalArticleResearch

Abstract

© 2019, Institute of Mathematical Statistics. All rights reserved. In this article, we consider the stochastic wave equation on R+ × R, driven by a linear multiplicative space-time homogeneous Gaussian noise whose temporal and spatial covariance structures are given by locally integrable functions γ (in time) and f (in space), which are the Fourier transforms of tempered measures ν on R, respectively µ on 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.
Original languageEnglish
Article number106
JournalElectronic Journal of Probability
Volume24
DOIs
Publication statusPublished - 1 Jan 2019

Keywords

  • Gaussian noise
  • Malliavin calculus
  • Stochastic partial differential equations

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