| Full text | |
| Author(s): |
Total Authors: 3
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| 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
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| 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: | 13/07699-0 - Research, Innovation and Dissemination Center for Neuromathematics - NeuroMat |
| Grantee: | Oswaldo Baffa Filho |
| Support Opportunities: | Research Grants - Research, Innovation and Dissemination Centers - RIDC |
| FAPESP's process: | 13/10101-9 - Localization of random walks in random environment and molecular spiders |
| Grantee: | Christophe Frédéric Gallesco |
| Support Opportunities: | Regular Research Grants |
| FAPESP's process: | 15/09094-3 - Stochastic chains with long memory |
| Grantee: | Alexsandro Giacomo Grimbert Gallo |
| Support Opportunities: | Regular Research Grants |