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

Yu Miao

• 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.