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

We investigate the convergence of McKean-Vlasov diffusions in a nonconvex landscape. These processes are linked to nonlinear partial differential equations. According to our previous results, there are at least three stationary measures…

We develop a general framework for establishing non-uniqueness of stationary measures for stochastically forced dynamical systems possessing an almost surely invariant submanifold. Our main abstract result provides sufficient conditions for…

We study the notion of stochastic stability with respect to diffusive perturbations for flows with smooth invariant measures. We investigate the question fully for non-singular flows on the circle. We also show that volume-preserving flows…

Given the significance of physical measures in understanding the complexity of dynamical systems as well as the noisy nature of real-world systems, investigating the stability of physical measures under noise perturbations is undoubtedly a…

In this article, we study stochastic partial differential equations with two reflecting walls, driven by space-time white noise with non-constant diffusion coefficients under periodic boundary conditions. The existence and uniqueness of…

In the paper, stationary measures of stochastic differential equations with jumps are considered. Under some general conditions, existence of stationary measures is proved through Markov measures and Lyapunov functions. Moreover, for two…

Statistical invariance of Wiener increments under SO(n) rotations provides a notion of gauge transformation of state-dependent Brownian motion. We show that the stochastic dynamics of non gauge-invariant systems is not unambiguously…

We study the invariant measures of infinite systems of stochastic differential equations (SDEs) indexed by the vertices of a regular tree. These invariant measures correspond to Gibbs measures associated with certain continuous…

This paper deals with the existence and limiting behavior of invariant measures of the stochastic Landau-Lifshitz-Bloch equation driven by linear multiplicative noise and additive noise defined in the entire space $\mathbb{R}^d$ for…

We carry out a comprehensive linear stability analysis of active Brownian particle systems around a constant homogeneous state. These scalar models, being important prototypes for the continuous description of active matter, are…

We investigate the unique stationary measure of a positive recurrent reflecting Brownian motion in the upper half-plane, where the direction of reflection is constant on each half-axis. The Laplace transform of the stationary distribution…

We consider some reaction-diffusion equations describing systems with the nonlocal consumption of resources and the intraspecific competition. Sharp conditions on the coefficients are obtained to ensure the stability and instability of…

In this paper we characterise the global stability, global boundedness and recurrence of solutions of a scalar nonlinear stochastic differential equation. The differential equation is a perturbed version of a globally stable autonomous…

In this paper, the development of a mathematical method is presented to explore spatially non-uniform phases with no long-range order in mathematical models of first order phase transitions. We use essential results regarding the…

We introduce a model of self-propelled particles carrying out a Brownian motion with a diffusion coefficient which depends on the local density of particles within a certain finite radius. Numerical simulations show that in a range of…

The discrete self-trapping equation (DST) represents an useful model for several properties of one-dimensional nonlinear molecular crystals. The modulational instability of DST equation is discussed from a statistical point of view,…

We develop a formally exact technique for obtaining steady-state distributions of non-interacting active Brownian particles in a variety of systems. Our technique draws on results from the theory of two-way diffusion equations to solve the…

In this work, we present sufficient conditions for the existence of a stationary solution of an abstract stochastic Cauchy problem driven by an arbitrary cylindrical L\'evy process, and show that these conditions are also necessary if the…

We prove the existence of solutions to a non-linear, non-local, degenerate equation which was previously derived as the formal hydrodynamic limit of an active Brownian particle system, where the particles are endowed with a position and an…

This study deals with continuous limits of interacting one-dimensional diffusive systems, arising from stochastic distortions of discrete curves with various kinds of coding representations. These systems are essentially of a…