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 language | English |
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Article number | 106 |
Journal | Electronic Journal of Probability |
Volume | 24 |
DOIs | |
Publication status | Published - 1 Jan 2019 |
Keywords
- Gaussian noise
- Malliavin calculus
- Stochastic partial differential equations