Related papers: Ergodicity for infinite particle systems with loca…

We study ergodic properties of nonlinear Markov chains and stochastic McKean-Vlasov equations. For nonlinear Markov chains we obtain sufficient conditions for existence and uniqueness of an invariant measure and uniform ergodicity. We also…

This paper provides a new path method that can be used to determine when an ergodic continuous-time Markov chain on $\mathbb Z^d$ converges exponentially fast to its stationary distribution in $L^2$. Specifically, we provide general…

The quantitative long time behavior of absorbing, finite, irreducible Markov processes is considered. Via Doob transforms, it is shown that only the knowledge of the ratio of the values of the underlying first Dirichlet eigenvector is…

We obtain the lower bounds for ergodic convergence rates, including spectral gaps and convergence rates in strong ergodicity for time-changed symmetric L\'{e}vy processes by using harmonic function and reversible measure. As direct…

For affine processes on finite-dimensional cones, we give criteria for geometric ergodicity - that is exponentially fast convergence to a unique stationary distribution. Ergodic results include both the existence of exponential moments of…

Using a model Hamiltonian for a single-mode electromagnetic field interacting with a nonlinear medium, we show that quantum expectation values of subsystem observables can exhibit remarkably diverse ergodic properties even when the dynamics…

Any discrete quantum process is represented by a sequence of quantum channels. We consider ergodic quantum processes obtained by a map that takes the points along the trajectory of a discrete ergodic dynamical system to the space of quantum…

We give locally finite Markov trees in $L^p$-compact$,$ separable Hilbert$,$ supersymmetric process$:$ $[0,\infty)\!\times\!\mathbb{R}^{\lvert\mathcal{A}^{\otimes m}\rvert}/\mathcal{A}^{\otimes m}$ on quantum ${\rm…

The objective of this paper is to characterize the structure of the set $\Theta$ for a continuous ergodic upper probability $\mathbb{V}=\sup_{P\in\Theta}P$ (Theorem \ref {main result}): . $\Theta$ contains a finite number of ergodic…

We obtain a local central limit theorem for cocycles associated with a class of non abelian and non compact group extensions of Gibbs Markov maps. This class consists of multidimensional infinite dihedral groups. Unlike in the set up of the…

In this paper, we investigate ergodicity in total variation of the process $X_t$, related to a L\'evy-driven stochastic differential equation with unbounded coefficients, and describe the speed of convergence to the respective invariant…

We establish pointwise almost everywhere convergence for ergodic averages along polynomial sequences in nilpotent groups of step two of measure-preserving transformations on $\sigma$-finite measure spaces. We also establish corresponding…

In this work, we address ergodicity of smooth actions of finitely generated semi-groups on an m-dimensional closed manifold M. We provide sufficient conditions for such an action to be ergodic with respect to the Lebesgue measure. Our…

We construct ergodic probability measures with infinite metric entropy for typical continuous maps and homeomorphisms on compact manifolds. We also construct sequences of such measures that converge to a zero-entropy measure.

The exponential ergodicity of partially dissipative McKean-Vlasov SDEs in the \(L^1\)-Wasserstein distance has been extensively studied using asymptotic reflection coupling. However, the reflection coupling method is not applicable for the…

Given an irreducible subshift of finite type X, a subshift Y, a factor map \pi : X \to Y, and an ergodic invariant measure \nu on Y, there can exist more than one ergodic measure on X which projects to \nu and has maximal entropy among all…

This paper studies the f-ergodicity and its exponential convergence rate for continuous-time Markov chain. Assume f is square integrable, for reversible Markov chain, it is proved that the exponential convergence of f-ergodicity holds if…

In [11], employing the technique of noncommutative interpolation, a maximal ergodic theorem in noncommutative Lp-spaces, 1 < p < infinity, was established and, among other things, corresponding maximal ergodic inequalities and individual…

For a large class of transitive non-hyperbolic systems, we construct nonhyperbolic ergodic measures with entropy arbitrarily close to its maximal possible value. The systems we consider are partially hyperbolic with one-dimension central…

We analyze the conforming approximation of the time-harmonic Maxwell's equations using N\'ed\'elec (edge) finite elements. We prove that the approximation is asymptotically optimal, i.e., the approximation error in the energy norm is…