相关论文: Non uniqueness of stationary measures for self-sta…

Wright's delay differential equation is one of the prime examples of a fully nonlinear equation without an explicit solution and whose dynamics can be understood by analytic means. In this paper, we introduce stochastic perturbations by…

The results of this paper build upon those first obtained by Sznitman and Zeitouni in [11]. We establish, for spacial dimensions greater than two, the existence of a unique invariant measure for isotropic diffusions in random environment…

In this paper, we are concerned with long-time behavior of Euler-Maruyama schemes associated with a range of regime-switching diffusion processes. The key contributions of this paper lie in that existence and uniqueness of numerical…

We describe a two-dimensional model for active particles whose self-propulsion speed is not fixed, but varies in time, and whose motion is subject to both translational and rotational diffusion. In the conventional treatment of active…

We develop a theory of optimal transport for stationary random measures with a focus on stationary point processes and construct a family of distances on the set of stationary random measures. These induce a natural notion of interpolation…

Some recent developments in the analysis of long-time behaviors of stochastic solutions of nonlinear conservation laws driven by stochastic forcing are surveyed. The existence and uniqueness of invariant measures are established for…

The paper is concerned with the existence and uniqueness of a strong solution to a two-dimensional backward stochastic Navier-Stokes equation with nonlinear forcing, driven by a Brownian motion. We use the spectral approximation and the…

Stochastic motion of particles in a highly unstable potential generates a number of diverging trajectories leading to undefined statistical moments of the particle position. This makes experiments challenging and breaks down a standard…

In this work we investigate the long-time behavior, that is the existence and characterization of invariant measures as well as convergence of transition probabilities, for Markov processes obtained as the unique mild solution to stochastic…

Properties of systems driven by white non-Gaussian noises can be very different from these systems driven by the white Gaussian noise. We investigate stationary probability densities for systems driven by $\alpha$-stable L\'evy type noises,…

The work deals with establishing the solvability of a system of integro-differential equations in the situation of the double scale anomalous diffusion. Each equation of such system involves the sum of the two negative Laplace operators…

We consider a stochastic electroconvection model describing the nonlinear evolution of a surface charge density in a two-dimensional fluid with additive stochastic forcing. We prove the existence and uniqueness of solutions and we show that…

An active Brownian particle is a minimal model for a self-propelled colloid in a dissipative environment. Experiments and simulations show that, in the presence of boundaries and obstacles, active Brownian particle systems approach…

Mass-conserving reaction-diffusion systems with bistable nonlinearity are considered under general assumptions. The existence of stationary solutions with a single internal transition layer in such reaction-diffusion systems is shown using…

Stimulated by experimental progress in high energy physics and astrophysics, the unification of relativistic and stochastic concepts has re-attracted considerable interest during the past decade. Focusing on the framework of special…

Random diffeomorphisms with bounded absolutely continuous noise are known to possess a finite number of stationary measures. We discuss dependence of stationary measures on an auxiliary parameter, thus describing bifurcations of families of…

In systems with overdamped dynamics, the Lorentz force reduces the diffusivity of a Brownian particle in the plane perpendicular to the magnetic field. The anisotropy in diffusion implies that the Fokker-Planck equation for the probabiliy…

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…

In this paper, we establish large deviation principle for the strong solution of a doubly nonlinear PDE driven by small multiplicative Brownian noise. Motononicity arguments and the weak convergence approach have been exploited in the…

In this work, we are concerned with existence and uniqueness of invariant measures for path-dependent random diffusions and their time discretizations. The random diffusion here means a diffusion process living in a random environment…