Related papers: Explicit criteria for several types of ergodicity
A class of nonlinear ARCH processes is introduced and studied. The existence of a strictly stationary and $\beta$-mixing solution is established under a mild assumption on the density of the underlying independent process. We give…
In this paper, we first introduce and define several new information divergences in the space of transition matrices of finite Markov chains which measure the discrepancy between two Markov chains. These divergences offer natural…
In this article, we discuss subgeometric ergodicity of a class of regime-switching diffusion processes. We derive conditions on the drift and diffusion coefficients, and the switching mechanism which result in subgeometric ergodicity of the…
Spatial birth-and-death processes with time dependent rates are obtained as solutions to certain stochastic equations. The existence, uniqueness, uniqueness in law and the strong Markov property of unique solutions are proven when the…
It has been established under very general conditions that the ergodic properties of Markov processes are inherited by their conditional distributions given partial information. While the existing theory provides a rather complete picture…
We study a class of dynamical systems generated by random substitutions, which contains both intrinsically ergodic systems and instances with several measures of maximal entropy. In this class, we show that the measures of maximal entropy…
We introduce a new definition of exponential family of Markov chains, and show that many characteristic properties of the usual exponential family of probability distributions are properly extended to Markov chains. The method of…
We develop and implement new probabilistic strategy for proving exponential ergodicity for interacting diffusion processes on unbounded lattice. The concept of the solution used is rather weak as we construct the process in infinite…
This article studies the quasi-stationary behaviour of absorbed one-dimensional diffusion processes with killing on $[0,\infty)$. We obtain criteria for the exponential convergence to a unique quasi-stationary distribution in total…
We study the nature and mechanisms of broken ergodicity (BE) in specific random walk models corresponding to diffusion on random potential surfaces, in both one and high dimension. Using both rigorous results and nonrigorous methods, we…
We consider the well-known problem of the computation of the (limiting) time-dependent performance characteristics of one-dimensional continuous-time birth and death processes on $\mathbb{Z}$ with time varying and possible state-dependent…
In this paper, we present criteria for non-exponential ergodicity of continuous-time Markov chains on a countable state space. These criteria can be verified by examining the ratio of transition rates over certain paths. We applied this…
In this paper a concentration inequality is proved for the deviation in the ergodic theorem in the case of discrete time observations of diffusion processes. The proof is based on the geometric ergodicity property for diffusion processes.…
We suggest an approach to obtaining general two-sided bounds on the rate of convergence in terms of special "weighted" norms related to total variation. Some important classes of continuous-time Markov chains are considered:…
The joint ergodicity classification problem aims to characterize those sequences which are jointly ergodic along an arbitrary dynamical system if and only if they satisfy two natural, simpler-to-verify conditions on this system. These two…
By using the coupling technique, we present sufficient conditions for the exponential ergodicity of general continuous-state nonlinear branching processes in both the $L^1$-Wasserstein distance and the total variation norm, where the drift…
The birth-death process is a special type of continuous-time Markov chain with index set $\mathbb{N}$. Its resolvent matrix can be fully characterized by a set of parameters $(\gamma, \beta, \nu)$, where $\gamma$ and $\beta$ are…
We describe the full exit boundary of random walks on homogeneous trees, in particular, on the free groups. This model exhibits a phase transition, namely, the family of Markov measures under study loses ergodicity as a parameter of the…
The main substance of the paper concerns the growth rate and the classification (ergodicity, transience) of a family of random trees. In the basic model, new edges appear according to a Poisson process of parameter $\lambda$ and leaves can…
An approach to analyse the properties of a particle system is to compare it with different processes to understand when one of them is larger than other ones. The main technique for that is coupling, which may not be easy to construct. We…