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Regular g-measures are not always Gibbsian

Dublin Core		PKP Metadata Items	Metadata for this Document
1.	Title	Title of document	Regular g-measures are not always Gibbsian
2.	Creator	Author's name, affiliation, country	Roberto Fernandez; University of Utrecht; Netherlands
2.	Creator	Author's name, affiliation, country	Sandro Gallo; Universidade Estadual de Campinas; Brazil
2.	Creator	Author's name, affiliation, country	Gregory Maillard; CMI-LATP, Aix-Marseille University; France
3.	Subject	Discipline(s)
3.	Subject	Keyword(s)	Discrete-time stochastic processes, $g$-measures, chains with complete connections, non-Gibbsianness, chains with variable-length memory
3.	Subject	Subject classification	60G10, 82B20, 37A05
4.	Description	Abstract	Regular g-measures are discrete-time processes determined by conditional expectations with respect to the past. One-dimensional Gibbs measures, on the other hand, are fields determined by simultaneous conditioning on past and future. For the Markovian and exponentially continuous cases both theories are known to be equivalent. Its equivalence for more general cases was an open problem. We present a simple example settling this issue in a negative way: there exist $g$-measures that are continuous and non-null but are not Gibbsian. Our example belongs, in fact, to a well-studied family of processes with rather nice attributes: It is a chain with variable-length memory, characterized by the absence of phase coexistence and the existence of a visible renewal scheme
5.	Publisher	Organizing agency, location
6.	Contributor	Sponsor(s)
7.	Date	(YYYY-MM-DD)	2011-11-20
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/1681
10.	Identifier	Digital Object Identifier	10.1214/ECP.v16-1681
11.	Source	Journal/conference title; vol., no. (year)	Electronic Communications in Probability; Vol 16
12.	Language	English=en
14.	Coverage	Geo-spatial location, chronological period, research sample (gender, age, etc.)
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