New results on asymptotic independence of random elements (Q2684711)

Two sequences \((X_{n}),(Y_{n})\) of random elements of the same probability space are said to be asymptotic independent if the joint distributions \( P_{(X_{n},Y_{n})}\) approach \(P_{X_{n}}\times P_{Y_{n}}\) in some sense as \( n\rightarrow \infty \). In the paper the authors consider 5 different definitions and in section 2 they study relationships/connections between these 5 definitions. Section 3 discusses the stability of the definitions under transformations.\ Section 4 focuses on the case where one of the marginals is tight. Section 5 is devoted to the case where the random elements belong to the space of sequences and in the case where the joint distributions are Gaussian. Some open questions are presented at the end of the paper.