TY - JOUR
T1 - Gaussian density estimates for solutions to quasi-linear stochastic partial differential equations
AU - Nualart, David
AU - Quer-Sardanyons, Lluís
PY - 2009/11/1
Y1 - 2009/11/1
N2 - In this paper we establish lower and upper Gaussian bounds for the solutions to the heat and wave equations driven by an additive Gaussian noise, using the techniques of Malliavin calculus and recent density estimates obtained by Nourdin and Viens in [17]. In particular, we deal with the one-dimensional stochastic heat equation in [0, 1] driven by the space-time white noise, and the stochastic heat and wave equations in Rd (d ≥ 1 and d ≤ 3, respectively) driven by a Gaussian noise which is white in time and has a general spatially homogeneous correlation. © 2009 Elsevier B.V. All rights reserved.
AB - In this paper we establish lower and upper Gaussian bounds for the solutions to the heat and wave equations driven by an additive Gaussian noise, using the techniques of Malliavin calculus and recent density estimates obtained by Nourdin and Viens in [17]. In particular, we deal with the one-dimensional stochastic heat equation in [0, 1] driven by the space-time white noise, and the stochastic heat and wave equations in Rd (d ≥ 1 and d ≤ 3, respectively) driven by a Gaussian noise which is white in time and has a general spatially homogeneous correlation. © 2009 Elsevier B.V. All rights reserved.
KW - Gaussian bounds
KW - Malliavin calculus
KW - Spatially homogeneous Gaussian noise
KW - Stochastic partial differential equations
U2 - 10.1016/j.spa.2009.09.001
DO - 10.1016/j.spa.2009.09.001
M3 - Article
SN - 0304-4149
VL - 119
SP - 3914
EP - 3938
JO - Stochastic Processes and their Applications
JF - Stochastic Processes and their Applications
ER -