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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.)

The Shortest Possible Return Time of ss-Mixing Processes

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Abadi, Miguel [1] ; Gallo, Sandro [2] ; Rada-Mora, Erika Alejandra [3]
Total Authors: 3
[1] Univ Sao Paulo, Inst Matemat & Estat, Sao Paulo - Brazil
[2] Univ Fed Sao Carlos, Dept Estat, Sao Paulo - Brazil
[3] Univ Fed ABC, Ctr Matemat Computacao & Cognicao, Sao Bernardo Do Campo, SP - Brazil
Total Affiliations: 3
Document type: Journal article
Source: IEEE TRANSACTIONS ON INFORMATION THEORY; v. 64, n. 7, p. 4895-4906, JUL 2018.
Web of Science Citations: 1

We consider a stochastic process and a given n-string. We study the shortest possible return time (or shortest return path) of the string over all the realizations of process starting from this string. For a beta-mixing process having complete grammar, and for each size n of the strings, we approximate the distribution of this short return (properly re-scaled) by a non-degenerated distribution. Under mild conditions on the beta coefficients, we prove the existence of the limit of this distribution to a non-degenerated distribution. We also prove that ergodicity is not enough to guaranty this convergence. Finally, we present a connection between the shortest return and the Shannon entropy, showing that maximum of the re-scaled variables grow as the matching function of Wyner and Ziv. (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
FAPESP's process: 15/09094-3 - Stochastic chains with long memory
Grantee:Alexsandro Giacomo Grimbert Gallo
Support Opportunities: Regular Research Grants