Stability of a random diffusion with nonlinear drift
type: Item
instance of: scholarly article
title: Stability of a random diffusion with nonlinear drift
zbMATH Open document ID: 1071.60070
published in: Statistics \& Probability Letters
publication date: 2005-04-21T00:00:00Z
review text: The author considers a strong Markov process, \((X(t),Z(t))\), with state space \({\mathbb R}^d\times N\) (\(N\) is finite), such that \(X(t)\) satisfies a stochastic differential equation with a rather general nonlinear drift, and \(Z(t)\) is a continuous-time Markov chain with state space \(N\). The author shows how to construct the coupling of \((X(t),Z(t))\) and itself; with the help of these results, Feller continuity, as well as the existence and uniqueness of invariant measure, are proved for \((X(t),Z(t))\). By using the Foster-Lyapunov inequality and coupling, the author proves the convergence in the total variation norm of the transition probability of \((X(t),Z(t))\) to the invariant measure as \(t\to\infty\) (the stability of \((X(t),Z(t))\) in total variation).
reviewed by: Alexander Mitrophanov
Mathematics Subject Classification ID: 60J60
zbMATH DE Number: 2159990
zbMATH Keywords: coupling
zbMATH Keywords: Feller continuity
zbMATH Keywords: total variation
zbMATH Keywords: Foster-Lyapunov inequality
author: Fubao Xi
MaRDI profile type: Publication
full work available at URL: j.spl.2004.03.010
OpenAlex ID: W2095380615
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DOI: 10.1016/J.SPL.2004.03.010
description: scientific article; zbMATH DE number 2159990