Related papers: Ergodicity for regime-switching neutral stochastic…
This paper contains a very simple and general proof that eigenfunctions of quantizations of classically ergodic systems become uniformly distributed in phase space. This ergodicity property of eigenfunctions f is shown to follow from a…
In this paper we study a system of stochastic differential equations with dissipative nonlinearity which arise in certain neurobiology models. Besides proving existence, uniqueness and continuous dependence on the initial datum, we shall be…
In this work, we shall consider the existence and uniqueness of stationary solutions to stochastic partial functional differential equations with additive noise in which a neutral type of delay is explicitly presented. We are especially…
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 introduce a framework for the control of discrete-time switched stochastic systems with uncertain distributions. In particular, we consider stochastic dynamics with additive noise whose distribution lies in an ambiguity set of…
For a class of linear switched systems in continuous time a controllability condition implies that state feedbacks allow to achieve almost sure stabilization with arbitrary exponential decay rates. This is based on the Multiplicative…
We study the ergodicity of stochastic real Ginzburg-Landau equation driven by additive $\alpha$-stable noises, showing that as $\alpha \in (3/2,2)$, this stochastic system admits a unique invariant measure. After establishing the existence…
This paper proposes a unified approach for studying global exponential stability of a general class of switched systems described by time-varying nonlinear functional differential equations. Some new delay-independent criteria of global…
Phase field evolutions are obtained by means of time discrete schemes, providing (or selecting) at each time step an equilibrium configuration of the system, which is usually computed by descent methods for the free energy (e.g.staggered…
We study (backward) stochastic differential equations with noise coming from a finite state Markov chain. We show that, for the solutions of these equations to be `Markovian', in the sense that they are deterministic functions of the state…
The statistical finite element method (StatFEM) is an emerging probabilistic method that allows observations of a physical system to be synthesised with the numerical solution of a PDE intended to describe it in a coherent statistical…
Eigenstate multifractality, a hallmark of non-interacting disordered metals, which may also be observed in many-body localized states, is characterized by anomalous slow dynamics and appears relevant for many areas of quantum physics, from…
For strongly positively recurrent countable state Markov shifts, we bound the distance between an invariant measure and the measure of maximal entropy in terms of the difference of their entropies. This extends an earlier result for…
Understanding how isolated quantum many-body systems thermalize remains a central question in modern physics. We study the onset of ergodicity in a two-dimensional disordered Heisenberg Floquet model using digital quantum simulation on…
We study one-dimensional, one-sided, nearest-neighbor Interacting Particle Systems (IPS) with positive rates and identify a criterion for ergodicity based on the presence of a long lived state a site can occupy. The criterion is that the…
A class of functional differential equations are investigated. Using the Girsanov-transformation argument we establish the quadratic transportation cost inequalities for a class of finite-dimensional neutral functional stochastic…
In this paper, we establish some sufficient conditions for the existence of stable random periodic solutions of stochastic differential equations and ergodicity in the random periodic regime. The techniques involve the existence of Lyapunov…
For the purpose of clarifying a new approach to understanding quantum entanglement using thermofield dynamics (TFD), entanglement entropies of non-equilibrium finite-spin systems are examined for both traditional and extended cases. The…
The paper deals with a class of cooperative functional differential equations (FDEs) with infinite delay, for which sufficient conditions for persistence and permanence are established. Here, the persistence refers to all solutions with…
In this paper, we introduce a new kind of reflected backward stochastic differential equations (RBSDEs) driven by a martingale, in a Markov chain model, but not driven by Brownian motion, and give existence and uniqueness results for the…