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Recurrence for branching Markov chains

Dublin Core		PKP Metadata Items	Metadata for this Document
1.	Title	Title of document	Recurrence for branching Markov chains
2.	Creator	Author's name, affiliation, country	Sebastian Müller; Technische Universität Graz
3.	Subject	Discipline(s)
3.	Subject	Keyword(s)	spectral radius, branching Markov chains, recurrence, transience, strong recurrence, positive recurrence
3.	Subject	Subject classification	60J10, 60J80
4.	Description	Abstract	The question of recurrence and transience of branching Markov chains is more subtle than for ordinary Markov chains; they can be classified in transience, weak recurrence, and strong recurrence. We review criteria for transience and weak recurrence and give several new conditions for weak recurrence and strong recurrence. These conditions make a unified treatment of known and new examples possible and provide enough information to distinguish between weak and strong recurrence. This represents a step towards a general classification of branching Markov chains. In particular, we show that in homogeneous cases weak recurrence and strong recurrence coincide. Furthermore, we discuss the generalization of positive and null recurrence to branching Markov chains and show that branching random walks on $Z$ are either transient or positive recurrent.
5.	Publisher	Organizing agency, location
6.	Contributor	Sponsor(s)	partially supported by FWF (Austrian Science Fund) project P19115-N18 and DFG (German Research Foundation) project MU 2868/1-1
7.	Date	(YYYY-MM-DD)	2008-11-24
8.	Type	Status & genre	Peer-reviewed Article
8.	Type	Type
9.	Format	File format	PDF
10.	Identifier	Uniform Resource Identifier	http://ecp.ejpecp.org/article/view/1424
10.	Identifier	Digital Object Identifier	10.1214/ECP.v13-1424
11.	Source	Journal/conference title; vol., no. (year)	Electronic Communications in Probability; Vol 13
12.	Language	English=en
14.	Coverage	Geo-spatial location, chronological period, research sample (gender, age, etc.)
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