Related papers: Elliptic stochastic partial differential equations…

Stochastic fractionally dissipative quasi-geostrophic type equation on $R^d$ with a multiplicative Gaussian noise is considered. We prove the existence of a martingale solution. In the 2D sub-critical case we prove also the pathwise…

We consider stochastic non-linear diffusion equations with a highly singular diffusivity term and multiplicative gradient-type noise. We study existence and uniqueness of non-negative variational solutions in terms of stochastic variational…

In this paper, we establish existence and uniqueness of strong solutions for a stochastic differential equation driven by an additive noise given by the sum of two correlated fractional Brownian sheets with different Hurst parameters. Our…

We study a class of linear first and second order partial differential equations driven by weak geometric $p$-rough paths, and prove the existence of a unique solution for these equations. This solution depends continuously on the driving…

In this paper we deal with the problem of the existence and the uniqueness of a solution for one dimensional reflected backward stochastic differential equations with two strictly separated barriers when the generator is allowing a…

The technique of stochastic solutions, previously used for deterministic equations, is here proposed as a solution method for partial differential equations driven by distribution-valued noises.

In this paper, we study reflected differential equations driven by continuous paths with finite $p$-variation ($1\le p<2$) and $p$-rough paths ($2\le p<3$) on domains in Euclidean spaces whose boundaries may not be smooth. We define…

We formulate stochastic partial differential equations on Riemannian manifolds, moving surfaces, general evolving Riemannian manifolds (with appropriate assumptions) and Riemannian manifolds with random metrics, in the variational setting…

The aim of this work is to prove existence and uniqueness of $L^{2}-$solutions of stochastic fractional partial differential equations in one spatial dimension. We prove also the equivalence between several notions of $L^{2}-$solutions. The…

We study the stochastic nonlinear Schroedinger equations with linear multiplicative noise, particularly in the defocusing mass-critical and energy-critical cases. For general initial data, we prove the global existence and uniqueness of…

The elliptic 2-Hessian equation is a fully nonlinear partial differential equation (PDE) that is related to intrinsic curvature for three dimensional manifolds. We introduce two numerical methods for this PDE: the first is provably…

In this paper we show the existence and uniqueness of a solution for a stochastic differential equation driven by an additive noise which is the sum of two fractional Brownian motions with different Hurst parameters. The proofs are based on…

A multiscale analysis of 1D stochastic bistable reaction-diffusion equations with additive noise is carried out w.r.t. travelling waves within the variational approach to stochastic partial differential equations. It is shown with explicit…

We prove existence and uniqueness of the solution of a stochastic shell--model. The equation is driven by an infinite dimensional fractional Brownian--motion with Hurst--parameter $H\in (1/2,1)$, and contains a non--trivial coefficient in…

In this paper, we consider a system of $k$ second order non-linear stochastic partial differential equations with spatial dimension $d \geq 1$, driven by a $q$-dimensional Gaussian noise, which is white in time and with some spatially…

In this paper, we study a class of stochastic partial differential equations (SPDEs) driven by space-time fractional noises. Our method consists in studying first the nonlocal SPDEs and showing then the convergence of the family of these…

We investigate a stochastic partial differential equation with second order elliptic operator in divergence form, having a piecewise constant diffusion coefficient, and driven by a space-time white noise. We introduce a notion of weak…

In this paper we extend previous work of Galleas and the author to elliptic SOS models. We demonstrate that the dynamical reflection algebra can be exploited to obtain a functional equation characterizing the partition function of an…

We prove the existence and uniqueness of mild solution for the stochastic partial differential equation $$\left(\partial^\alpha - \textit{B} \right) u(t,x)= u(t,x) \cdot \dot{W}(t,x),$$ where $$\alpha \in (1/2, 1)\cup(1, 2);$$ $\textit{B}$…

In this article, we consider non-smooth time-dependent domains and single-valued, smoothly varying directions of reflection at the boundary. In this setting, we first prove existence and uniqueness of strong solutions to stochastic…