Abstract. Complete convergence and the Marcinkiewicz-Zygmund strong law of large numbers for sequences of m-pairwise negatively quadrant dependent (m-PNQD) random variables is studied in this paper. The results obtained extend and improve the corresponding theorems of Choi and Sung ([4]) and Hu et al. ([9]). A version of the Kolmogorov strong law of large numbers for sequences of m-PNQD random ...

In this paper we introduce the concept of asymptotically almost negatively associated random variables in a Hilbert space and obtain the strong law of large numbers for a strictly stationary asymptotically almost negatively associated sequence of H-valued random variables with zero means and finite second moments. As an application we prove a strong law of large numbers for a linear process gen...

Inequalities are at the heart of mathematical and statistical theory. No inequality is completely perfect, but the Hájek-Rényi inequality, which is the main subject of this thesis, is arguably the closest to absolute perfection of all the inequalities within all theories of probability. It has many applications in proving limit theorems, and examples of these are presented in this thesis. The s...