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Three Kinds of Geometric Convergence for Markov Chains and the Spectral Gap Property

Dublin Core		PKP Metadata Items	Metadata for this Document
1.	Title	Title of document	Three Kinds of Geometric Convergence for Markov Chains and the Spectral Gap Property
2.	Creator	Author's name, affiliation, country	Wolfgang Stadje; University of Osnabrück; Germany
2.	Creator	Author's name, affiliation, country	Achim Wübker; University of Osnabrück; Germany
3.	Subject	Discipline(s)
3.	Subject	Keyword(s)	Markov chains, geometric ergodicity, speed of convergence
3.	Subject	Subject classification	60J10
4.	Description	Abstract	In this paper we investigate three types of convergence for geometrically ergodic Markov chains (MCs) with countable state space, which in general lead to different `rates of convergence'. For reversible Markov chains it is shown that these rates coincide. For general MCs we show some connections between their rates and those of the associated reversed MCs. Moreover, we study the relations between these rates and a certain family of isoperimetric constants. This sheds new light on the connection of geometric ergodicity and the so-called spectral gap property, in particular for non-reversible MCs, and makes it possible to derive sharp upper and lower bounds for the spectral radius of certain non-reversible chains
5.	Publisher	Organizing agency, location
6.	Contributor	Sponsor(s)	DFG
7.	Date	(YYYY-MM-DD)	2011-04-20
8.	Type	Status & genre	Peer-reviewed Article
8.	Type	Type
9.	Format	File format	PDF
10.	Identifier	Uniform Resource Identifier	http://ejp.ejpecp.org/article/view/900
10.	Identifier	Digital Object Identifier	10.1214/EJP.v16-900
11.	Source	Journal/conference title; vol., no. (year)	Electronic Journal of Probability; Vol 16
12.	Language	English=en
14.	Coverage	Geo-spatial location, chronological period, research sample (gender, age, etc.)
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