Nguyen Van Quang

Complete convergence for arrays of rowwise independent random variables and fuzzy random variables in convex combination spaces

The aim of this study is to establish the complete convergence for arrays of rowwise independent random variables and fuzzy random variables in convex combination space. Our results not only generalize related previously reported results but also improve them. Some illustrative examples are provided.

Strong laws of large numbers for adapted arrays of set-valued and fuzzy-valued random variables in Banach space

In this paper, we establish some strong laws of large numbers for double adapted arrays of set-valued and fuzzy-valued random variables in separable Banach space. Our results are obtained with and without conditionally compactly uniformly integrable hypothesis, and they are more general than some related results.

Strong laws for blockwise martingale difference arrays in Banach spaces

In this paper, we introduce the concepts of blockwise adapted array, blockwise martingale difference array, and establish some strong laws of large numbers for blockwise adapted arrays and blockwise martingale difference arrays. We also provide some characterizations of p-smoothable Banach spaces.

A Hájek-Rényi-Type Maximal Inequality and Strong Laws of Large Numbers for Multidimensional Arrays

A Hájek-Rényi-type maximal inequality is established for multidimensional arrays of random elements. Using this result, we establish some strong laws of large numbers for multidimensional arrays. We also provide some characterizations of Banach spaces.

Negative association and negative dependence for random upper semicontinuous functions, with applications

The aim of this paper is to construct the notions of negative association and negative dependence for random upper semicontinuous functions. Besides giving some properties for these notions, we obtain inequalities which form maximal inequality and Hajek-Renyis type inequality. In addition, some laws of large numbers are established under various settings and they are extensions for corresponding ones in the literature.

On the weak law of large numbers for double adapted arrays of random elements in p -uniformly smooth Banach space

The aim of this paper is to establish the weak law of large numbers with and wihtout random indices for double arrays of random elements of p-uniformly smooth Banach space. Our result is more general and stronger than some well-known ones.