Dynamic uniqueness for stochastic chains with unbounded memory

Autor(es)

Gallesco, Christophe ^[1] ; Gallo, Sandro ^[2] ; Takahashi, Daniel Y. ^[3]

Afiliação do(s) autor(es)

^[1] Univ Estadual Campinas, Inst Matemat Estat & Ciencia Comp, Dept Estat, Campinas, SP - Brazil

^[2] Univ Fed Sao Carlos, Dept Estat, Sao Carlos, SP - Brazil

^[3] Princeton Univ, Princeton Neurosci Inst, Princeton, NJ 08544 - USA

• Tipo de documento: Artigo Científico
• Fonte: Stochastic Processes and their Applications; v. 128, n. 2, p. 689-706, FEB 2018.
• Citações Web of Science: 2

Resumo

We say that a probability kernel exhibits dynamic uniqueness (DU) if all the stochastic chains starting from a fixed past coincide on the future tail a-algebra. Our first theorem is a set of properties that are pairwise equivalent to DU which allow us to understand how it compares to other more classical concepts. In particular, we prove that DU is equivalent to a weak-l(2) summability condition on the kernel. As a corollary to this theorem, we prove that the Bramson-Kalikow and the long-range Ising models both exhibit DU if and only if their kernels are l(2) summable. Finally, if we weaken the condition for DU, asking for coincidence on the future sigma-algebra for almost every pair of pasts, we obtain a condition that is equivalent to beta-mixing (weak-Bernoullicity) of the compatible stationary chain. As a consequence, we show that a modification of the weak-l(2) summability condition on the kernel is equivalent to the beta-mixing of the compatible stationary chain. (C) 2017 Elsevier B.V. All rights reserved. (AU)

• Processo FAPESP: 13/07699-0 - Centro de Pesquisa, Inovação e Difusão em Neuromatemática - NeuroMat
• Beneficiário: Oswaldo Baffa Filho
• Modalidade de apoio: Auxílio à Pesquisa - Centros de Pesquisa, Inovação e Difusão - CEPIDs
• Processo FAPESP: 13/10101-9 - Localização de passeios aleatórios em meio aleatório e aranhas moleculares
• Beneficiário: Christophe Frédéric Gallesco
• Modalidade de apoio: Auxílio à Pesquisa - Regular
• Processo FAPESP: 15/09094-3 - Cadeias estocásticas de longo alcance
• Beneficiário: Alexsandro Giacomo Grimbert Gallo
• Modalidade de apoio: Auxílio à Pesquisa - Regular