Asymptotic properties of nonlinear autoregressive Markov processes with state-dependent switching
type: Item
instance of: scholarly article
title: Asymptotic properties of nonlinear autoregressive Markov processes with state-dependent switching
zbMATH Open document ID: 1200.60059
author: B. E. Eshmatov
published in: Journal of Multivariate Analysis
publication date: 2010-05-05T00:00:00Z
review text: The paper studies asymptotic properties of nonlinear autoregressive (AR) processes with state-dependent switching \(({X_n},{Z_n})\), defined by \({X_n} = {f_{{Z_n}}}({X_{n - 1}}) + {\varepsilon _n}\), \({X_n} \in {\mathbb{R}^d}\) and \(P[{Z_n} = l\left| {{Z_{n - 1}} = k,{X_{n - 1}} = x] = {p_{kl}}(x)} \right.\), \(k,l \in \{ 1,2,\dots,{n_0}\} ,x \in {\mathbb{R}^d}\). The error process \(\{ {\varepsilon _n}\} \)is assumed to be a sequence of independent and identically distributed random vectors. Section 2 proves Feller and strong Feller continuity for AR processes. Section 3 proves its aperiodicity and investigates geometric ergodicity. A number of illustrative examples are provided in Sections 3-5.
reviewed by: Oleg K. Zakusilo
Mathematics Subject Classification ID: 60J05
Mathematics Subject Classification ID: 60K37
zbMATH DE Number: 5704004
zbMATH Keywords: nonlinear autoregressive process
zbMATH Keywords: two-component Markov process
zbMATH Keywords: state-dependent switching
zbMATH Keywords: ergodicity
zbMATH Keywords: geometric ergodicity
MaRDI profile type: Publication
full work available at URL: j.jmva.2009.12.006
OpenAlex ID: W2069834906
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DOI: 10.1016/J.JMVA.2009.12.006
description: scientific article; zbMATH DE number 5704004