Related papers: Evolution systems of measures for stochastic flows
The aim of this paper is to study the dynamical behavior of non-autonomous stochastic lattice systems with Markovian switching. We first show existence of an evolution system of measures of the stochastic system. We then study the pullback…
We investigate the long-time behavior of solutions to a stochastically forced one-dimensional Navier-Stokes system, describing the motion of a compressible viscous fluid, in the case of linear pressure law. We prove existence of an…
In this paper, we seek to understand the behavior of dynamical systems that are perturbed by a parameter that changes discretely in time. If we impose certain conditions, we can study certain embedded systems within a hybrid system as…
The limiting stability of invariant probability measures of time homogeneous transition semigroups for autonomous stochastic systems has been extensively discussed in the literature. In this paper we initially initiate a program to study…
One calls attention to the fact that the stochastic physical systems are not random completely. They have both random and regular components of their evolution. Dynamic system is considered to be a special case of physical system with…
In finite-dimensional dynamical systems, stochastic stability provides the selection of physical relevant measures from the myriad invariant measures of conservative systems. That this might also apply to infinite-dimensional systems is the…
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…
We examine the question of existence and uniqueness of evolution systems of measures for non-autonomous Ornstein-Uhlenbeck-type processes with jumps. In particular, we give examples where we explicitly compute the densities of such families…
We consider long-time behavior of dynamical systems perturbed by a small noise. Under certain conditions, a slow component of such a motion, which is most important for long- time evolution, can be described as a motion on the cone of…
We study the long-time behaviour of a stochastic Allen-Cahn-Navier-Stokes system modelling the dynamics of binary mixtures of immiscible fluids. The model features two stochastic forcings, one on the velocity in the Navier-Stokes equation…
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…
This article deals with invariant manifolds for infinite dimensional random dynamical systems with different time scales. Such a random system is generated by a coupled system of fast-slow stochastic evolutionary equations. Under suitable…
We present an application of the theory of stochastic processes to model and categorize non-equilibrium physical phenomena. The concepts of uniformly continuous probability measures and modular evolution lead to a systematic hierarchical…
This article develops mathematical formalisms and provides numerical methods for studying the evolution of measures in nonsmooth dynamical systems using the continuity equation. The nonsmooth dynamical system is described by an evolution…
We consider an electrodiffusion model that describes the intricate interplay of multiple ionic species with a two-dimensional, incompressible, viscous fluid subjected to stochastic additive noise. This system involves nonlocal nonlinear…
We analyze ecological systems that are influenced by random environmental fluctuations. We first provide general conditions which ensure that the species coexist and the system converges to a unique invariant probability measure (stationary…
In the first part of the note we analyze the long time behaviour of a two dimensional stochastic Navier--Stokes equations system on a torus with a degenerate, one dimensional noise. In particular, for some initial data and noises we…
In this paper, a new decay estimate for a class of stochastic evolution equations with weakly dissipative drifts is established, which directly implies the uniqueness of invariant measures for the corresponding transition semigroups.…
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…
The aim of this paper is to study the dynamical behavior of non-autonomous stochastic hybrid systems with delays. By general Krylov-Bogolyubov's method, we first obtain the sufficient conditions for the existence of an evolution system of…