REGULAR G-MEASURES ARE NOT ALWAYS GIBBSIAN

Autor(es)

Fernandez, Roberto ^[1] ; Gallo, Sandro ^[2] ; Maillard, Gregory ^[3]

Afiliação do(s) autor(es)

^[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

• Tipo de documento: Artigo Científico
• Fonte: Electronic Communications in Probability; v. 16, p. 732-740, NOV 20 2011.
• Citações Web of Science: 9

Resumo

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)

• Processo FAPESP: 09/09809-1 - Processos estocásticos com memória de alcance variável: Monge-Kantorovich, reamostragem e sistemas markovianos de partículas
• Beneficiário: Alexsandro Giacomo Grimbert Gallo
• Linha de fomento: Bolsas no Brasil - Pós-Doutorado