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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)


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Fernandez, Roberto [1] ; Gallo, Sandro [2] ; Maillard, Gregory [3]
Total Authors: 3
[1] Univ Utrecht, Dept Math, NL-3508 TA Utrecht - Netherlands
[2] Univ Estadual Campinas, Inst Matemat Estat & Comp Cient, BR-13083859 Campinas, SP - Brazil
[3] Aix Marseille Univ, CMI LATP, F-13453 Marseille 13 - France
Total Affiliations: 3
Document type: Journal article
Source: Electronic Communications in Probability; v. 16, p. 732-740, NOV 20 2011.
Web of Science Citations: 9

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. (AU)

FAPESP's process: 09/09809-1 - Stochastic processes with variable length memory: Monge-Kantorovich problem, bootstrap and particle systems
Grantee:Alexsandro Giacomo Grimbert Gallo
Support Opportunities: Scholarships in Brazil - Post-Doctoral