Related papers: Spatial asymptotics for the parabolic Anderson mod…
In this paper we study the linear stochastic heat equation, also known as parabolic Anderson model, in multidimension driven by a Gaussian noise which is white in time and it has a correlated spatial covariance. Examples of such covariance…
We consider the linear stochastic heat equation on $\mathbb{R}^\ell$, driven by a Gaussian noise which is colored in time and space. The spatial covariance satisfies general assumptions and includes examples such as the Riesz kernel in any…
This paper studies the one-dimensional parabolic Anderson model driven by a Gaussian noise which is white in time and has the covariance of a fractional Brownian motion with Hurst parameter $H \in (\frac{1}{4}, \frac{1}{2})$ in the space…
This paper studies the nonlinear one-dimensional stochastic heat equation driven by a Gaussian noise which is white in time and which has the covariance of a fractional Brownian motion with Hurst parameter 1/4\textless{}H\textless{}1/2 in…
In this paper, we study spatial averages for the parabolic Anderson model in the Skorohod sense driven by rough Gaussian noise, which is colored in space and time. We include the case of a fractional noise with Hurst parameters $H_0$ in…
The aim of this paper is to study the $d$-dimensional stochastic heat equation with a multiplicative Gaussian noise which is white in space and it has the covariance of a fractional Brownian motion with Hurst parameter $% H\in (0,1)$ in…
Partially motivated by the recent papers of Conus, Joseph and Khoshnevisan [Ann. Probab. 41 (2013) 2225-2260] and Conus et al. [Probab. Theory Related Fields 156 (2013) 483-533], this work is concerned with the precise spatial asymptotic…
In this article, we consider fractional stochastic wave equations on $\mathbb R$ driven by a multiplicative Gaussian noise which is white/colored in time and has the covariance of a fractional Brownian motion with Hurst parameter…
In this note, we consider the parabolic Anderson model on $\mathbb{R}_{+} \times \mathbb{R}$, driven by a Gaussian noise which is fractional in time with index $H_0>1/2$ and fractional in space with index $0<H<1/2$ such that $H_0+H>3/4$.…
In this article, we consider the stochastic wave equation on the real line driven by a linear multiplicative Gaussian noise, which is white in time and whose spatial correlation corresponds to that of a fractional Brownian motion with Hurst…
In this article, we study the hyperbolic Anderson model in dimension 1, driven by a time-independent rough noise, i.e. the noise associated with the fractional Brownian motion of Hurst index $H \in (1/4,1/2)$. We prove that, with…
We consider the continuous parabolic Anderson model with the Gaussian fields under the measure-valued initial conditions, the covariances of which are nonhomogeneous in time and fractional rough in space. We mainly study the spatial…
In this paper, we study the stochastic heat equation with a general multiplicative Gaussian noise that is white in time and colored in space. Both regularity and strict positivity of the densities of the solution have been established. The…
In this article, we study the stochastic wave equation in arbitrary spatial dimension $d$, with a multiplicative term of the form $\sigma(u)=u$, also known in the literature as the Hyperbolic Anderson Model. This equation is perturbed by a…
A parameter estimation problem is considered for a one-dimensional stochastic wave equation driven by additive space-time Gaussian white noise. The estimator is of spectral type and utilizes a finite number of the spatial Fourier…
In this note we consider the parabolic Anderson model in one dimension with time-independent fractional noise $\dot{W}$ in space. We consider the case $H<\frac{1}{2}$ and get existence and uniqueness of solution. In order to find the…
In this article, we investigate the asymptotic behaviour of the spatial integral of the solution to the parabolic Anderson model with time independent noise in dimension $d\geq 1$, as the domain of the integral becomes large. We consider 3…
We consider a system of $d$ non-linear stochastic heat equations driven by an $m$-dimensional space-time white noise on $\mathbb{R}_+\times \mathbb{R}$. In this paper we study the asymptotic behavior of spatial averages over large intervals…
In this article, we study the Parabolic Anderson Model driven by a space-time homogeneous Gaussian noise on $\mathbb{R}_{+} \times \mathbb{R}^d$, whose covariance kernels in space and time are locally integrable non-negative functions,…
In [HHL+17] the authors showed existence and uniqueness of solutions to the nonlinear one-dimensional stochastic heat equation driven by a Gaussian noise that is white in time and rougher than white in space (in particular, its covariance…