Related papers: The stochastic reflection problem with multiplicat…
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…
The aim of these notes is to give an overview of the current results about existence and uniqueness of solutions for the stochastic Euler equation driven by a Brownian noise in a two-dimensional bounded domain.
Additive or multiplicative stationary noise recently became an important issue in applied fields such as microscopy or satellite imaging. Relatively few works address the design of dedicated denoising methods compared to the usual white…
This work aims to investigate the existence of ergodic invariant measures and its uniqueness, associated with obstacle problems governed by a T-monotone operator defined on Sobolev spaces and driven by a multiplicative noise in a bounded…
A change of variables is introduced to reduce certain nonlinear stochastic evolution equations with multiplicative noise to the corresponding deterministic equation. The result is then used to investigate a stochastic porous medium…
This study addresses limited attention allocation in a stochastic linear quadratic system with multiplicative noise. Our approach enables strategic resource allocation to enhance noise estimation and improve control decisions. We provide…
We mainly investigate the log-Harnack inequality for the reflected stochastic partial differential equation driven by multiplicative noises based on the gradient estimate of the associated Markov semigroup. To do it, the penalization method…
We establish a quadratic transportation cost inequality under the uniform norm for solutions to mean reflected stochastic partial differential equations, a new type of equation in which the compensating reflection part depends not on the…
In this note, we establish a bi-parameter linear localization of the one-dimensional stochastic wave equation with a multiplicative space-time white noise forcing.
The paper deals with the problem of finding sparse solutions to systems of polynomial equations possibly perturbed by noise. In particular, we show how these solutions can be recovered from group-sparse solutions of a derived system of…
We consider a stochastic partial differential equation with reflection at 0 and with the constraint of conservation of the space average. The equation is driven by the derivative in space of a space--time white noise and contains a double…
We establish the existence and uniqueness of strong solutions, in both the PDE and probabilistic sense, for a broad class of nonlinear stochastic partial differential equations (SPDEs) on a bounded domain $\mathscr{O}\subset \mathbb{R}^d$…
We perturb with an additive Gaussian white noise the Hamiltonian system associated to a cubic anharmonic oscillator. The stochastic system is assumed to start from initial conditions that guarantee the existence of a periodic solution for…
Starting from the simple point process model of 1/f noise we derive a stochastic nonlinear differential equation for the signal exhibiting 1/f noise in any desirably wide range of frequency. A stochastic differential equation (the general…
We propose a two-point flux approximation finite-volume scheme for a stochastic non-linear parabolic equation with a multiplicative noise. The time discretization is implicit except for the stochastic noise term in order to be compatible…
We consider linear stochastic differential-algebraic equations with constant coefficients and additive white noise. Due to the nature of this class of equations, the solution must be defined as a generalised process (in the sense of Dawson…
In the pathwise stochastic calculus framework, the paper deals with the general study of equations driven by an additive Gaussian noise, with a drift function having an infinite limit at point zero. An ergodic theorem and the convergence of…
This paper is intended to give a probabilistic representation for stochastic viscosity solution of semi-linear reflected stochastic partial differential equations with nonlinear Neumann boundary condition. We use it connection with…
We consider inverse problems for non-linear hyperbolic and elliptic equations and give an introduction to the method based on the multiple linearization, or on the construction of artificial sources, to solve these problems. The method is…
In this paper, we establish lower and upper Gaussian bounds for the probability density of the mild solution to the stochastic heat equation with multiplicative noise and in any space dimension. The driving perturbation is a Gaussian noise…