| Full text | |
| Author(s): |
Total Authors: 3
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| Affiliation: | [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
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| Document type: | Journal article |
| Source: | IEEE TRANSACTIONS ON INFORMATION THEORY; v. 64, n. 7, p. 4895-4906, JUL 2018. |
| Web of Science Citations: | 1 |
| Abstract | |
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 type: | Regular Research Grants |
| FAPESP's process: | 15/09094-3 - Stochastic chains with long memory |
| Grantee: | Alexsandro Giacomo Grimbert Gallo |
| 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 |