Related papers: Exponential mixing for some SPDEs with L\'evy nois…

We prove exponential convergence to the invariant measure, in the total variation norm, for solutions of SDEs driven by $\alpha$-stable noises in finite and in infinite dimensions. Two approaches are used. The first one is based on Harris…

We study a class of discrete-time random dynamical systems with compact phase space. Assuming that the deterministic counterpart of the system in question possesses a dissipation property, its linearisation is approximately controllable,…

By a coupling method, we prove that a family of stochastic partial differential equations (SPDEs) driven by highly degenerate pure jump L\'evy noises are exponential mixing. These pure jump L\'evy noises include $\alpha$-stable process with…

We study convergence to the invariant measure for a class of semilinear stochastic evolution equations driven by L\'evy noise, including the case of cylindrical noise. For a certain class of equations we prove the exponential rate of…

We modify the coupling method established in [22, 20] and develop a technique to prove the exponential mixing of a 2D stochastic system forced by degenerate Levy noises. In particular, these Levy noises include $\alpha$-stable noises (0 <…

We prove that well posed quasilinear equations of parabolic type, perturbed by bounded nondegenerate random forces, are exponentially mixing for a large class of random forces.

We establish a general criterion which ensures exponential mixing of parabolic Stochastic Partial Differential Equations (SPDE) driven by a non additive noise which is white in time and smooth in space. We apply this criterion on two…

Explicit coupling property and gradient estimates are investigated for the linear evolution equations on Hilbert spaces driven by an additive cylindrical L\'evy process. The results are efficiently applied to establish the exponential…

In this paper, we discuss exponential mixing property for Markovian semigroups generated by segment processes associated with several class of retarded Stochastic Differential Equations (SDEs) which cover SDEs with…

In the present work, we establish the approximation of nonlinear stochastic partial differential equation (SPDE) driven by cylindrical {\alpha}-stable L\'evy processes via modulation or amplitude equations. We study SPDEs with a cubic…

We prove the exponential convergence to a unique invariant measure for locally damped nonlinear Schr\"odinger equations, perturbed by bounded noise acting on only two Fourier modes. To tackle the lack of smoothing effect, we introduce…

We proved the existence of an infinite dimensional stochastic system driven by white $\alpha$-stable noises ($1<\alpha \leq 2$), and prove this system is strongly mixing. Our method is by perturbing Ornstein-Uhlenbeck $\alpha$-stable…

We develop a general framework for studying ergodicity of order-preserving Markov semigroups. We establish natural and in a certain sense optimal conditions for existence and uniqueness of the invariant measure and exponential convergence…

In this paper, we establish the law of the iterated logarithm for a wide class of non-stationary, continuous-time Markov processes evolving on Polish spaces. Specifically, our result applies to certain additive functionals of processes…

This paper establishes strong and weak convergence rates for slow-fast systems driven by $\alpha$-stable processes with jump coefficients. Unlike existing studies on multiscale systems driven by additive L\'{e}vy white noise, our model…

We prove gradient estimates for transition Markov semigroups $(P_t)$ associated to SDEs driven by multiplicative Brownian noise having possibly unbounded $C^1$-coefficients, without requiring any monotonicity type condition. In particular,…

We consider parabolic stochastic partial differential equations driven by white noise in time. We prove exponential convergence of the transition probabilities towards a unique invariant measure under suitable conditions. These conditions…

We consider a class of semilinear stochastic evolution equations driven by an additive cylindrical stable noise.We investigate structural properties of the solutions like Markov, irreducibility, stochastic continuity, Feller and strong…

We study stochastic partial differential equations of the reaction-diffusion type. We show that, even if the forcing is very degenerate (i.e. has not full rank), one has exponential convergence towards the invariant measure. The convergence…

The paper deals with the problem of long-time asymptotic behaviour of solutions for classes of ODEs and PDEs, perturbed by stationary noises. The latter are not assumed to be $\delta$-correlated in time, so that the evolution in question is…