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Examples of Convergence and Non-convergence of Markov Chains Conditioned Not To Die

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1.	Title	Title of document	Examples of Convergence and Non-convergence of Markov Chains Conditioned Not To Die
2.	Creator	Author's name, affiliation, country	Saul Jacka; University of Warwick
2.	Creator	Author's name, affiliation, country	Jon Warren; University of Warwick
3.	Subject	Discipline(s)	Mathematics
3.	Subject	Keyword(s)	Conditioned Markov process, evanescent process, Martin boundary, Martin topology, superharmonic function, Choquet representation, star, Kolmogorov K2 chain
3.	Subject	Subject classification	Primary: 60J50 Secondary: 60B10, 60G99, 60J27, 60J45, 60J55
4.	Description	Abstract	In this paper we give two examples of evanescent Markov chains which exhibit unusual behaviour on conditioning to survive for large times. In the first example we show that the conditioned processes converge vaguely in the discrete topology to a limit with a finite lifetime, but converge weakly in the Martin topology to a non-Markovian limit. In the second example, although the family of conditioned laws are tight in the Martin topology, they possess multiple limit points so that weak convergence fails altogether.
5.	Publisher	Organizing agency, location
6.	Contributor	Sponsor(s)
7.	Date	(YYYY-MM-DD)	2001-10-03
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/100
10.	Identifier	Digital Object Identifier	10.1214/EJP.v7-100
11.	Source	Journal/conference title; vol., no. (year)	Electronic Journal of Probability; Vol 7
12.	Language	English=en	en
14.	Coverage	Geo-spatial location, chronological period, research sample (gender, age, etc.)
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