Lluís Quer-Sardanyons
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View article: Convergence in law for quasi-linear SPDEs
Convergence in law for quasi-linear SPDEs Open
We consider the quasi-linear stochastic wave and heat equations in $\mathbb{R}^d$ with $d\in \{1,2,3\}$ and $d\geq 1$, respectively, and perturbed by an additive Gaussian noise which is white in time and has a homogeneous spatial correlati…
View article: Weak approximation of the complex Brownian sheet from a Lévy sheet and applications to SPDEs
Weak approximation of the complex Brownian sheet from a Lévy sheet and applications to SPDEs Open
We consider a Lévy process in the plane and we use it to construct a family of complex-valued random fields that we show to converge in law, in the space of continuous functions, to a complex Brownian sheet. We apply this result to obtain …
View article: SPDEs with linear multiplicative fractional noise: continuity in law\n with respect to the Hurst index
SPDEs with linear multiplicative fractional noise: continuity in law\n with respect to the Hurst index Open
In this article, we consider the one-dimensional stochastic wave and heat\nequations driven by a linear multiplicative Gaussian noise which is white in\ntime and behaves in space like a fractional Brownian motion with Hurst index\n$H\\in (…
View article: SPDEs with fractional noise in space: Continuity in law with respect to the Hurst index
SPDEs with fractional noise in space: Continuity in law with respect to the Hurst index Open
In this article, we consider the quasi-linear stochastic wave and heat equations on the real line and with an additive Gaussian noise which is white in time and behaves in space like a fractional Brownian motion with Hurst index $H\in (0,1…
View article: Weak approximation of the complex Brownian sheet from a L\\'evy sheet and\n applications to SPDEs
Weak approximation of the complex Brownian sheet from a L\\'evy sheet and\n applications to SPDEs Open
We consider a L\\'evy process in the plane and we use it to construct a family\nof complex-valued random fields that we show to converge in law, in the space\nof continuous functions, to a complex Brownian sheet. We apply this result to\no…
View article: Absolute continuity of solutions to reaction-diffusion equations with\n multiplicative noise
Absolute continuity of solutions to reaction-diffusion equations with\n multiplicative noise Open
We prove absolute continuity of the law of the solution, evaluated at fixed\npoints in time and space, to a parabolic dissipative stochastic PDE on\n$L^2(G)$, where $G$ is an open bounded domain in $\\mathbb{R}^d$ with smooth\nboundary. Th…
View article: Existence of density for the stochastic wave equation with space-time homogeneous Gaussian noise
Existence of density for the stochastic wave equation with space-time homogeneous Gaussian noise Open
In this article, we consider the stochastic wave equation on $\\mathbb{R} _{+} \\times \\mathbb{R} $, driven by a linear multiplicative space-time homogeneous Gaussian noise whose temporal and spatial covariance structures are given by loc…
View article: SPDEs with fractional noise in space: continuity in law with respect to\n the Hurst index
SPDEs with fractional noise in space: continuity in law with respect to\n the Hurst index Open
In this article, we consider the quasi-linear stochastic wave and heat\nequations on the real line and with an additive Gaussian noise which is white\nin time and behaves in space like a fractional Brownian motion with Hurst index\n$H\\in …
View article: A fully discrete approximation of the one-dimensional stochastic heat equation
A fully discrete approximation of the one-dimensional stochastic heat equation Open
A fully discrete approximation of the one-dimensional stochastic heat equation driven by multiplicative space–time white noise is presented. The standard finite difference approximation is used in space and a stochastic exponential method …
View article: Hölder continuity for the Parabolic Anderson Model with space-time homogeneous Gaussian noise
Hölder continuity for the Parabolic Anderson Model with space-time homogeneous Gaussian noise Open
In this article, we consider the Parabolic Anderson Model with constant initial condition, driven by a space-time homogeneous Gaussian noise, with general covariance function in time and spatial spectral measure satisfying Dalang's conditi…
View article: Existence of density for the stochastic wave equation with space-time homogeneous Gaussian noise
Existence of density for the stochastic wave equation with space-time homogeneous Gaussian noise Open
In this article, we consider the stochastic wave equation on $\mathbb{R}_{+} \times \mathbb{R}$, driven by a linear multiplicative space-time homogeneous Gaussian noise whose temporal and spatial covariance structures are given by locally …
View article: A fully discrete approximation of the one-dimensional stochastic heat equation
A fully discrete approximation of the one-dimensional stochastic heat equation Open
A fully discrete approximation of the one-dimensional stochastic heat equation driven by multiplicative space-time white noise is presented. The standard finite difference approximation is used in space and a stochastic exponential method …
View article: SPDEs with affine multiplicative fractional noise in space with index $\frac{1}{4}\langle H\langle\frac{1}{2}$
SPDEs with affine multiplicative fractional noise in space with index $\frac{1}{4}\langle H\langle\frac{1}{2}$ Open
In this article, we consider the stochastic wave and heat equations on $\\mathbb{R}$ with non-vanishing initial conditions, driven by a Gaussian noise which is white in time and behaves in space like a fractional Brownian motion of index $…