Related papers: A skew stochastic heat equation

In this paper, we study the following stochastic heat equation \[ \partial_tu=\mathcal{L} u(t,x)+\dot{B},\quad u(0,x)=0,\quad 0\le t\le T,\quad x\in\mathbb{R}d, \] where $\mathcal{L}$ is the generator of a L\'evy process $X$ taking value in…

We consider a one-dimensional harmonic crystal with conservative noise, in contact with two stochastic Langevin heat baths at different temperatures. The noise term consists of collisions between neighbouring oscillators that exchange their…

In this paper, we study the stochastic nonlinear heat equations (SNLH) and stochastic nonlinear wave equations (SNLW) on two-dimensional torus driven by a subordinate cylindrical Brownian noise, which we define by the time-derivative of a…

We explore the small mass limit of a stochastic wave equation (SWE) driven by cylindrical $\alpha$-stable noise, where $\alpha\in (1,2)$, and prove that it converges to a stochastic heat equation. We establish its well-posedness, and in…

We consider a system of $d$ linear stochastic heat equations driven by an additive infinite-dimensional fractional Brownian noise on the unit circle $S^1$. We obtain sharp results on the H\"older continuity in time of the paths of the…

In this paper, we investigate the stochastic damped Burgers equation with multiplicative noise defined on the entire real line. We demonstrate the existence and uniqueness of a mild solution to the stochastic damped Burgers equation and…

A stochastic heat equation on an unbounded nested fractal driven by a general stochastic measure is investigated. Existence, uniqueness and continuity of the mild solution are proved provided that the spectral dimension of the fractal is…

We study long-term behavior and stationary distributions for stochastic heat equations forced simultaneously by a multiplicative noise and an independent additive noise with the same distribution. We prove that nontrivial space-time…

We consider a stochastic delay differential equation driven by a general Levy process. Both, the drift and the noise term may depend on the past, but only the drift term is assumed to be linear. We show that the segment process is…

In this paper we study properties of solutions to stochastic differential equations with Sobolev diffusion coefficients and singular drifts. The properties we study include stability with respect to the coefficients, weak differentiability…

This is a preliminary announcement of results in the PhD. thesis of the first author concerning the nonlinear stochastic heat equation in the spatial domain $\R$, driven by space-time white noise. A central special case is the parabolic…

We introduce and study a new class of non-Archimedean stochastic pseudodifferential equations. These equations are the non-Archimedean counterparts of the classical stochastic heat equations. We show the existence and uniqueness of mild…

We study the space-time nonlinear fractional stochastic heat equation driven by a space-time white noise, \begin{align*} \partial_t^\beta u(t,x)=-(-\Delta)^{\alpha/2}u(t,x)+I_t^{1-\beta}\Big[\sigma(u(t,x))\dot{W}(t,x)\Big],\ \ t>0, \ x\in…

The aim of this paper is to establish the almost sure asymptotic behavior as the space variable becomes large, for the solution to the one spatial dimensional stochastic heat equation driven by a Gaussian noise which is white in time and…

In this paper we establish the strong existence, pathwise uniqueness and a comparison theorem to a stochastic partial differential equation driven by Gaussian colored noise with non-Lipschitz drift, H\"older continuous diffusion…

We study here the approximation by a finite-volume scheme of a heat equation forced by a Lipschitz continuous multiplicative noise in the sense of It\^o. More precisely, we consider a discretization which is semi-implicit in time and a…

We study stochastic heat equations driven by a class of L\'evy processes: du = \De u dt + g dX_t \quad in \quad \bR^d_T, \qquad u(0,x)= 0 \quad in \quad x \in \bR^d. We prove the corresponding estimate \[\norm{u}_{\bH_p^k(\RT)} \le c(p,T)…

We consider a stochastic Camassa-Holm equation driven by a one-dimensional Wiener process with a first order differential operator as diffusion coefficient. We prove the existence and uniqueness of local strong solutions of this equation.…

Based on the system heat bath approach where the bath is nonlinearly modulated by an external Gaussian random force, we propose a new microscopic model to study directed motion in the overdamped limit for a nonequilibrium open system.…

The stochastic Gross-Pitaevskii equation is used as a model to describe Bose-Einstein condensation at positive temperature. The equation is a complex Ginzburg Landau equation with a trapping potential and an additive space-time white noise.…