Hájek-Rényi inequality for dependent random variables in Hilbert space and applications

• Yu Miao ^[1]
  1. [1] Henan Normal University

     Henan Normal University

     China

     
• Localización: Revista de la Unión Matemática Argentina, ISSN 0041-6932, ISSN-e 1669-9637, Vol. 53, Nº. 1, 2012, págs. 101-112
• Idioma: inglés
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• Resumen

  • In this paper, we obtain some Hájek-Rényi inequalities for sequences of Hilbert valued random variables which are associated, negatively associated and φ-mixing. As applications, we give some almost sure convergence theorems for these dependent sequences in Hilbert space. These results extend and improve some well-known results.