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96 papers · 1 filter
Quantitative central limit theorems for the parabolic Anderson model driven by colored noises
David Nualart, Panqiu Xia, Guangqu Zheng
In this paper, we study the spatial averages of the solution to the parabolic Anderson model driven by a space-time Gaussian homogeneous noise that is colored in time and space. We…
Regularization of differential equations by two fractional noises
David Nualart, Ercan Sönmez
In this paper we show the existence and uniqueness of a solution for a stochastic differential equation driven by an additive noise which is the sum of two fractional Brownian moti…
The hyperbolic Anderson model: Moment estimates of the Malliavin derivatives and applications
Raluca M. Balan, David Nualart, Lluís Quer-Sardanyons +1
In this article, we study the hyperbolic Anderson model driven by a space-time \emph{colored} Gaussian homogeneous noise with spatial dimension . Under mild assumptions, we…
Quantitative normal approximations for the stochastic fractional heat equation
Obayda Assaad, David Nualart, Ciprian A. Tudor +1
In this article we present a {\it quantitative} central limit theorem for the stochastic fractional heat equation driven by a a general Gaussian multiplicative noise, including the…
Spatial ergodicity of stochastic wave equations in dimensions 1,2 and 3
David Nualart, Guangqu Zheng
In this note, we study a large class of stochastic wave equations with spatial dimension less than or equal to . Via a soft application of Malliavin calculus, we establish that…
Spatial stationarity, ergodicity and CLT for parabolic Anderson model with delta initial condition in dimension
Davar Khoshnevisan, David Nualart, Fei Pu
Suppose that is the solution to a -dimensional parabolic Anderson model with delta initial condition and driven by a Gaussian noise tha…