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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.)

Almost sure convergence of the clustering factor in alpha-mixing processes

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Abadi, Miguel [1] ; Saussol, Benoit [2]
Total Authors: 2
[1] Univ Sao Paulo, Inst Matemat & Estat, BR-05508090 Sao Paulo - Brazil
[2] Univ Bretagne Occidentale, LMBA CNRS UMR 6205, F-29238 Brest - France
Total Affiliations: 2
Document type: Journal article
Source: Stochastics and Dynamics; v. 16, n. 3, SI JUN 2016.
Web of Science Citations: 1

Abadi and Saussol (2011) have proved that the first time a dynamical system, starting from its equilibrium measure, hits a target set A has approximately an exponential law. These results hold for systems satisfying the alpha-mixing condition with rate function alpha decreasing to zero at any rate. The parameter of the exponential law is the product lambda(A)mu(A), where the latter is the measure of the set A; only bounds for lambda(A) were given. In this note we prove that, if the rate function a decreases algebraically and if the target set is a sequence of nested cylinders sets A(n)(x) around a point x, then lambda(A(n)) converges to one for almost every point x. As a byproduct, we obtain the corresponding result for return times. (AU)

FAPESP's process: 14/19805-1 - Statistics of extreme events and dynamics of recurrence
Grantee:Miguel Natalio Abadi
Support Opportunities: Regular Research Grants
FAPESP's process: 13/07699-0 - Research, Innovation and Dissemination Center for Neuromathematics - NeuroMat
Grantee:Jefferson Antonio Galves
Support Opportunities: Research Grants - Research, Innovation and Dissemination Centers - RIDC