相关论文: Non-linear Young equations in the plane and pathwi…

We consider reaction-diffusion equations that are stochastically forced by a small multiplicative noise term. We show that spectrally stable travelling wave solutions to the deterministic system retain their orbital stability if the…

This paper focuses on the long-term behavior of solutions to nonlinear stochastic Fokker-Planck equations driven by common noise, where the drift term has a linear dependence on the measure. These equations, which describe the evolution of…

The Cahn-Hilliard/Allen-Cahn equation with noise is a simplified mean field model of stochastic microscopic dynamics associated with adsorption and desorption-spin flip mechanisms in the context of surface processes. For such an equation we…

In this paper we study some stability criteria for some semilinear integral equations with a function as initial condition and with additive noise, which is a Young integral that could be a functional of fractional Brownian motion. Namely,…

We investigate the validity and accuracy of weak-noise (saddle-point or instanton) approximations for piecewise-smooth stochastic differential equations (SDEs), taking as an illustrative example a piecewise-constant SDE, which serves as a…

A linear stochastic continuity equation with non-regular coefficients is considered. We prove existence and uniqueness of strong solution, in the probabilistic sense, to the Cauchy problem when the vector field has low regularity, in which…

This paper is concerned with developing and analyzing two novel implicit temporal discretization methods for the stochastic semilinear wave equations with multiplicative noise. The proposed methods are natural extensions of well-known…

In this work we perform rigorous small noise expansions to study the impact of stochastic forcing on the behaviour of planar travelling wave solutions to reaction-diffusion equations on cylindrical domains. In particular, we use a…

Semilinear stochastic evolution equations with multiplicative Poisson noise and monotone nonlinear drift are considered. We do not impose coercivity conditions on coefficients. A novel method of proof for establishing existence and…

This article is devoted to the study of the existence and uniqueness of mild solution to time- and space-fractional stochastic Burgers equation perturbed by multiplicative white noise. The required results are obtained by stochastic…

In this paper we construct a new type of noise of fractional nature that has a strong regularizing effect on differential equations. We consider an equation with this noise with a highly irregular coefficient. We employ a new method to…

We study a model of the motion by mean curvature of an (1+1) dimensional interface in a 2D Brownian velocity field. For the well-posedness of the model we prove existence and uniqueness for certain degenerate nonlinear stochastic evolution…

Existence, uniqueness, and regularity of a strong solution are obtained for stochastic PDEs with a colored noise $F$ and its super-linear diffusion coefficient: $$ du=(a^{ij}u_{x^ix^j}+b^iu_{x^i}+cu)dt+\xi|u|^{1+\lambda}dF, \quad…

We study ODEs with vector fields given by general Schwartz distributions, and we show that if we perturb such an equation by adding an "infinitely regularizing" path, then it has a unique solution and it induces an infinitely smooth flow of…

We study a stochastic Schr{\"o}dinger equation with a quadratic nonlinearity and a space-time fractional perturbation, in space dimension less than 3. When the Hurst index is large enough, we prove local well-posedness of the problem using…

In this work, we deal with the stochastic counterpart of the nonlocal Cahn-Hilliard equation with regular potential in a smooth bounded one-, two- or three-dimensional domain. The problem is endowed with homogeneous Neumann boundary…

The paper is concerned with spatial and time regularity of solutions to linear stochastic evolution equation perturbed by L\'evy white noise "obtained by subordination of a Gaussian white noise". Sufficient conditions for spatial continuity…

In this paper we present a general framework in which to rigorously study the effect of spatio-temporal noise on traveling waves and stationary patterns. In particular the framework can incorporate versions of the stochastic neural field…

This is an overview about natural sample spaces for differential equations driven by various noises. Appropriate sample spaces are needed in order to facilitate a random dynamical systems approach for stochastic differential equations. The…

We study the well solvability of nonlinear backward stochastic evolutionary equations driven by a space-time white noise. We first establish a novel a priori estimate for solution of linear backward stochastic evolutionary equations, and…