arXiv:1910.04243 Abstract | arXiv Analytics

arXiv:1910.04243 [math.PR]Abstract References Reviews Resources

Remarks on asymptotic independence

Published 2019-10-09Version 1

In this paper we introduce 5 natural definitions (AI-0) - (AI-4) of asymptotic independence (AI) of two sequences ($X_n$), ($Y_n$) of random elements. We discuss their basic properties, some simple connections between them and connections with properties of weak dependence. In particular, the case of tight sequences is considered in detail. Finally, in order to clarify the relationships between AI-0 - AI-4, we provide some counterexamples.

Comments: 20 pages

Categories: math.PR

Subjects: 60F99, 60G97, 60B10, 60B99

Keywords: asymptotic independence, tight sequences, weak dependence, natural definitions, simple connections

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