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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.)

Dynamic uniqueness for stochastic chains with unbounded memory

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Author(s):
Gallesco, Christophe [1] ; Gallo, Sandro [2] ; Takahashi, Daniel Y. [3]
Total Authors: 3
Affiliation:
[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
Total Affiliations: 3
Document type: Journal article
Source: Stochastic Processes and their Applications; v. 128, n. 2, p. 689-706, FEB 2018.
Web of Science Citations: 2
Abstract

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)

FAPESP's process: 13/10101-9 - Localization of random walks in random environment and molecular spiders
Grantee:Christophe Frédéric Gallesco
Support type: Regular Research Grants
FAPESP's process: 13/07699-0 - Research, Innovation and Dissemination Center for Neuromathematics - NeuroMat
Grantee:Jefferson Antonio Galves
Support type: Research Grants - Research, Innovation and Dissemination Centers - RIDC
FAPESP's process: 15/09094-3 - Stochastic chains with long memory
Grantee:Alexsandro Giacomo Grimbert Gallo
Support type: Regular Research Grants