Characterization of asymptotic statistical equivalent double and single sequences

This paper presents a series of four-dimensional matrix characterizations of statistically asymptotically equivalent double and single sequences. These characterizations begins with the presentation of definitions for asymptotically equivalent and asymptotically statistical equivalent of multiple L for double and single sequences. The type of questions we provided answers for are those of the following sort. What are the necessary and sufficient conditions on the entries A that ensure the preservation of statistically asymptotically equivalent rate of convergence.