Related papers: Ergodicity for regime-switching neutral stochastic…
We address stability of a class of Markovian discrete-time stochastic hybrid systems. This class of systems is characterized by the state-space of the system being partitioned into a safe or target set and its exterior, and the dynamics of…
We study the ergodic property of a continuous-state branching process with immigration and competition. The exponential ergodicity in a weighted total variation distance is proved under natural assumptions. The main theorem applies to…
We review recent progress in the study of infinite-dimensional stochastic differential equations with symmetry. This paper contains examples arising from random matrix theory.
These notes present an alternative approach to the asymptotic stability of stochastic partial differential equations driven by multiplicative noise, applicable to a wide range of dissipative systems. The method builds on general criteria…
Despite its long history, a canonical formulation of quantum ergodicity that applies to general classes of quantum dynamics, including driven systems, has not been fully established. Here we introduce and study a notion of quantum…
Recently, a number of authors have investigated the conditions under which a stochastic perturbation acting on an infinite dimensional dynamical system, e.g. a partial differential equation, makes the system ergodic and mixing. In…
This paper deals with existence and uniqueness, in viscosity sense, of a solution for a system of m variational partial differential inequalities with inter-connected obstacles. A particular case of this system is the deterministic version…
We study the long-term qualitative behavior of randomly perturbed dynamical systems. More specifically, we look at limit cycles of stochastic differential equations (SDE) with Markovian switching, in which the process switches at random…
We study a generic but simple non-integrable quantum {\em many-body} system of {\em locally} interacting particles, namely a kicked $t-V$ model of spinless fermions on 1-dim lattice (equivalent to a kicked Heisenberg XX-Z chain of 1/2…
We consider damped stochastic systems in a controlled (time-varying) quadratic potential and study their transition between specified Gibbs-equilibria states in finite time. By the second law of thermodynamics, the minimum amount of work…
The first motivation of this paper is to study stationarity and ergodic properties for a general class of time series models defined conditional on an exogenous covariates process. The dynamic of these models is given by an autoregressive…
In this paper, we propose a novel kind of numerical approximations to inherit the ergodicity of stochastic Maxwell equations. The key to proving the ergodicity lies in the uniform regularity estimates of the numerical solutions with respect…
This paper studies a system of $m$ variational inequalities with interconnected obstacles in infinite horizon associated to optimal multi-modes switching problems. Our main result is the existence and uniqueness of a continuous solution in…
Dark states are stationary states of a dissipative, Lindblad-type time evolution with zero von Neumann entropy, therefore representing examples of pure, steady quantum states. Non-equilibrium dynamics featuring a dark state recently gained…
In this paper, we concern with the ergodic linear-quadratic closed-loop optimal control problems, in which the state equation is the mean-field stochastic differential equation with periodic coefficients. We first study the asymptotic…
This paper studies explicit numerical approximations of the invariant probability measures (IPMs) for stochastic functional differential equations (SFDEs) with infinite delay under one-sided Lipschitz condition on the drift coefficient. To…
The main purpose of this work is to characterize the almost sure local structure stability of solutions to a class of linear stochastic partial functional differential equations (SPFDEs) by investigating the Lyapunov exponents and invariant…
We study a discrete version of a biaxial nematic liquid crystal model with external fields via an approach based on the solution of differential identities for the partition function. In the thermodynamic limit, we derive the free energy of…
Applying Zvonkin's transform, the exponential convergence in Wasserstein distance for a class of functional SDEs with H\"older continuous drift is obtained. This combining with log-Harnack inequality implies the same convergence in the…
This paper studies a system of multi-dimensional reflected backward stochastic differential equations with oblique reflections (RBSDEs for short) in infinite horizon associated to switching problems. The existence and uniqueness of the…