Ergodic properties of Markov processes

Copulas, Chaotic Processes and Time Series: a Survey

In this work we summarize some of recent and classical results on the role played by copulas in the analysis of chaotic processes and univariate time series. We review some aspects of the copulas related to chaotic process, its properties and applications. We also present a review on classical and modern approaches to understand the relationship among random variables in Markov processes as wel...

Ergodic Properties of Stationary, Markov, and Regenerative Processes

An Ergodic Control Problem for Constrained Diffusion Processes: Existence of Optimal Markov Control

An ergodic control problem for a class of constrained diffusion processes is considered. The goal is the almost sure minimization of long term cost per unit time. The main result of the paper is that there exists an optimal Markov control for the considered problem. It is shown that under the assumption of regularity of the Skorohod map and appropriate conditions on the drift coefficient the cl...

Ergodic properties for α-CIR models and a class of generalized Fleming-Viot processes

We discuss a Markov jump process regarded as a variant of the CIR (Cox-IngersollRoss) model and its infinite-dimensional extension. These models belong to a class of measure-valued branching processes with immigration, whose jump mechanisms are governed by certain stable laws. The main result gives a lower spectral gap estimate for the generator. As an application, a certain ergodic property is...

Ergodicity for Time Changed Symmetric Stable Processes

In this paper we study the ergodicity and the related semigroup property for a class of symmetric Markov jump processes associated with time changed symmetric α-stable processes. For this purpose, explicit and sharp criteria for Poincaré type inequalities (including Poincaré, super Poincaré and weak Poincaré inequalities) of the corresponding non-local Dirichlet forms are derived. Moreover, our...