The Shortest Possible Return Time of ss-Mixing Processes

Autor(es)

Abadi, Miguel ^[1] ; Gallo, Sandro ^[2] ; Rada-Mora, Erika Alejandra ^[3]

Afiliação do(s) autor(es)

^[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

• Tipo de documento: Artigo Científico
• Fonte: IEEE TRANSACTIONS ON INFORMATION THEORY; v. 64, n. 7, p. 4895-4906, JUL 2018.
• Citações Web of Science: 1

Resumo

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)

• Processo FAPESP: 14/19805-1 - Estatísticas para eventos extremos e dinâmica de recorrência
• Beneficiário: Miguel Natalio Abadi
• Linha de fomento: Auxílio à Pesquisa - Regular
• Processo FAPESP: 15/09094-3 - Cadeias estocásticas de longo alcance
• Beneficiário: Alexsandro Giacomo Grimbert Gallo
• Linha de fomento: Auxílio à Pesquisa - Regular
• Processo FAPESP: 13/07699-0 - Centro de Pesquisa, Inovação e Difusão em Neuromatemática - NeuroMat
• Beneficiário: Jefferson Antonio Galves
• Linha de fomento: Auxílio à Pesquisa - Centros de Pesquisa, Inovação e Difusão - CEPIDs