Hájek–Rényi inequality for m-asymptotically almost negatively associated random vectors in Hilbert space and applications

Abstract

Abstract In this paper, we obtain the Hájek–Rényi inequality and, as an application, we study the strong law of large numbers for H-valued m-asymptotically almost negatively associated random vectors with mixing coefficients {q(n),n≥1} $\{q(n), n\geq1\}$ such that ∑n=1∞q(n)2<∞ $\sum_{n=1}^{\infty}q(n)^{2}<\infty$.

Keywords

• Asymptotically almost negative association
• Hilbert space
• Hájek–Rényi inequality
• Strong law of large numbers
• Mixing coefficients