Related papers: Ergodicity and weak mixing for group-indexed infin…

The concept of weak ergodicity breaking is defined and studied in the context of deterministic dynamics. We show that weak ergodicity breaking describes a weakly chaotic dynamical system: a nonlinear map which generates subdiffusion…

This paper investigates the ergodicity of Markov--Feller semigroups on Polish spaces, focusing on very weak regularity conditions, particularly the Ces\`aro eventual continuity. First, it is showed that the Ces\`aro average of such…

In this paper we study the Poisson process over a $\sigma$-finite measure-space equipped with a measure preserving transformation or a group of measure preserving transformations. For a measure-preserving transformation $T$ acting on a…

The idea of a parsing of a stationary process according to a collection of words is introduced, and the basic framework required for the asymptotic analysis of these parsings is presented. We demonstrate how the pointwise ergodic theorem…

In ergodic theory, given sufficient conditions on the system, every weak mixing $\mathbb{N}$-action is strong mixing along a density one subset of $\mathbb{N}$. We ask if a similar statement holds in topological dynamics with density one…

We obtain a perfect sampling characterization of weak ergodicity for backward products of finite stochastic matrices, and equivalently, simultaneous tail triviality of the corresponding nonhomogeneous Markov chains. Applying these ideas to…

We consider a class of observation-driven Poisson count processes where the current value of the accompanying intensity process depends on previous values of both processes. We show under a contractive condition that the bivariate process…

The purpose of this paper is to prove a weak convergence result for empirical processes indexed in general classes of functions and with an underlying $\alpha$-mixing sequence of random variables. In particular the uniformly boundedness…

The aim of this paper is to prove ergodic decomposition theorems for probability measures quasi-invariant under Borel actions of inductively compact groups (Theorem 1) as well as for sigma-finite invariant measures (Corollary 1). For…

This work contains the following results: the trajectory fullness of the homoclinic groups, their connections with factors, K-property, weak multiple mixing; the ergodicity of the weakly homoclinic group for Gauss and Poisson actions; the…

Let $G$ be a closed permutation group on a countably infinite set $\Omega$, which acts transitively but not highly transitively. If $G$ is oligomorphic, has no algebraicity and weakly eliminates imaginaries, we prove that any probability…

Consider an invertible measure-preserving transformation of a probability space. A finite partition of the space is called weakly independent if there are infinitely many images of this partition under powers of the transformation that are…

This paper investigates the ergodicity of stochastic functional differential equations with jumps under the Wasserstein distance by the generalized coupling method. Two key conditions are verified. The first is verified by establishing an…

In the context of the long-standing issue of mixing in infinite ergodic theory, we introduce the idea of mixing for observables possessing an infinite-volume average. The idea is borrowed from statistical mechanics and appears to be…

The issue of relaxation has been addressed in terms of ergodic theory in the past. However, the application of that theory to models of physical interest is problematic, especially when dealing with relaxation to nonequilibrium steady…

We define a class of discrete abelian group extensions of rank-one transformations and establish necessary and sufficient conditions for these extensions to be power weakly mixing. We show that all members of this class are multiply…

A measure preserving action of a countably infinite group \Gamma is called totally ergodic if every infinite subgroup of \Gamma acts ergodically. For example, all mixing and mildly mixing actions are totally ergodic. This note shows that if…

We construct a rank one infinite measure preserving transformation $T$ such that for all sequences of nonzero integers $\{k_{1},..., k_{r}\}$, $T^{k_{1}}\times...\times T^{k_{r}}$ is ergodic.

We present a reachability based approach to establish unique ergodicity of non-linear filter processes where state space of a hidden Markov model is a compact Polish metric space and the observation space is a Polish metric space. We also…

We consider a point process sequence induced by a stationary symmetric alpha-stable (0 < alpha < 2) discrete parameter random field. It is easy to prove, following the arguments in the one-dimensional case in Resnick and Samorodnitsky…