On a unique ergodicity of some Markov processes
type: Item
instance of: scholarly article
title: On a unique ergodicity of some Markov processes
zbMATH Open document ID: 1244.60074
author: Rafał Kapica
author: Tomasz Szarek
author: Maciej Ślȩczka
published in: Potential Analysis
publication date: 2012-05-08T00:00:00Z
review text: The authors prove that any weakly irreducible e-process admits at most one invariant measure. The stochastic process on \(X\) given by a semigroup \((P_t)_{t\geq0}\) is called e-process if it satisfies the e-property: for any point \(x\in X\) and an arbitrary Lipschitz bounded function \(\phi: X\to \mathbb{R}\) the family \(\{P_t\phi(x)\}_{t\geq0}\) is equicontinuous in \(x\). Some application to time-homogeneous Markov process associated with a nonlinear heat equation driven by an impulsive noise is also given.
reviewed by: N. G. Gamkrelidze
Mathematics Subject Classification ID: 60J25
Mathematics Subject Classification ID: 60H15
Mathematics Subject Classification ID: 76N10
zbMATH DE Number: 6031715
zbMATH Keywords: Ergodicity of Markov families
zbMATH Keywords: e-process
zbMATH Keywords: invariant measures
zbMATH Keywords: stochastic heat equations
MaRDI profile type: Publication
full work available at URL: s11118-011-9242-0
OpenAlex ID: W2121446461
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DOI: 10.1007/S11118-011-9242-0
description: scientific article; zbMATH DE number 6031715