TY - JOUR
T1 - Existence of density for the stochastic wave equation with space-time homogeneous gaussian noise
AU - Balan, Raluca M.
AU - Quer-Sardanyons, Lluís
AU - Song, Jian
PY - 2019/1/1
Y1 - 2019/1/1
N2 - © 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.
AB - © 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.
KW - Gaussian noise
KW - Malliavin calculus
KW - Stochastic partial differential equations
UR - https://ddd.uab.cat/record/223686
U2 - https://doi.org/10.1214/19-EJP363
DO - https://doi.org/10.1214/19-EJP363
M3 - Article
VL - 24
JO - Electronic Journal of Probability
JF - Electronic Journal of Probability
SN - 1083-6489
M1 - 106
ER -