相关论文: A Singular Parabolic Anderson Model
The low-temperature behavior of the asymmetric single-impurity Anderson model is studied by diagrammatic methods resulting in analytically controllable approximations. We first discuss the ways one can simplify parquet equations in critical…
Collapse models including some external noise of unknown origin are routinely used to describe phenomena on the quantum-classical border; in particular, quantum measurement. Although containing nonlinear dynamics and thereby exposed to the…
This paper deals with the parametric inference for integrated signals embedded in an additive Gaussian noise and observed at deterministic discrete instants which are not necessarily equidistant. The unknown parameter is multidimensional…
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…
Numerical methods for stochastic partial differential equations typically estimate moments of the solution from sampled paths. Instead, we shall directly target the deterministic equations satisfied by the first and second moments, as well…
We study the two-dimensional stochastic nonlinear heat equation (SNLH) and stochastic damped nonlinear wave equation (SdNLW) with an exponential nonlinearity $\lambda\beta e^{\beta u }$, forced by an additive space-time white noise. We…
This paper addresses the detection of a stochastic process in noise from irregular samples. We consider two hypotheses. The \emph{noise only} hypothesis amounts to model the observations as a sample of a i.i.d. Gaussian random variables…
We study the effect of curvature on the Parabolic Anderson model by posing it over a Cartan-Hadamard manifold. We first construct a family of noises white in time and colored in space parameterized by a regularity parameter $\alpha$, which…
We study existence and uniqueness of weak solutions to (F) $\partial\_t u+ (-\Delta)^\alphau+h(t, u)=0 $ in $(0,\infty)\times\R^N$,with initial condition $u(0,\cdot)=\nu$ in $\R^N$, where $N\ge2$, the operator $(-\Delta)^\alpha$is the…
We propose and analyse a mechanism by which $\mathrm{CO}_2$-driven radiative forcing can increase Arctic temperature variability in a stochastic Sellers-type energy-balance model. Starting from a fast-slow formulation in which insolation is…
We study a wave equation in dimension $d\in \{1,2\}$ with a multiplicative space-time Gaussian noise. The existence and uniqueness of the Stratonovich solution is obtained under some conditions imposed on the Gaussian noise. The strategy is…
In the present note we show dynamical localization for an Anderson model with missing sites in a discrete setting at the bottom of the spectrum in arbitrary dimension $d$. In this model, the random potential is defined on a relatively dense…
We continue our study of intermittency for the parabolic Anderson equation $\partial u/\partial t = \kappa\Delta u + \xi u$, where $u\colon \Z^d\times [0,\infty)\to\R$, $\kappa$ is the diffusion constant, $\Delta$ is the discrete Laplacian,…
In this paper, we investigate a system of parabolic partial differential equations with unknown-dependent coefficients that integrates two models: an anisotropic orientation-adaptive denoising process in image processing and a phase-field…
The problem of existence of non-analytic (Griffith-like) contributions to the free energy of weakly disordered Ising ferromagnet is studied from the point of view of the replica theory. The consideration is done in terms of the usual random…
We study stability of solutions for a randomly driven and degenerately damped version of the Lorenz '63 model. Specifically, we prove that when damping is absent in one of the temperature components, the system possesses a unique invariant…
We consider existence and uniqueness issues for the initial value problem of parabolic equations $\partial_{t} u = {\rm div} A \nabla u$ on the upper half space, with initial data in $L^p$ spaces. The coefficient matrix $A$ is assumed to be…
We study the effect of Gaussian perturbations on a class of model hyperbolic partial differential equations with double symplectic characteristics in low spatial dimensions, extending some recent work in [5]. The coefficients of our partial…
In this work we develop a Bayesian setting to infer unknown parameters in initial-boundary value problems related to linear parabolic partial differential equations. We realistically assume that the boundary data are noisy, for a given…
An overdamped system with a linear restoring force and two multiplicative colored noises is considered. Noise amplitudes depend on the system state $x$ as $x$ and $|x|^{\alpha}$. An exactly soluble model of a system is constructed due to…