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Multivariate Generalizations of the q--Central Limit Theorem

Sabir Umarov·Constantino Tsallis
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Abstract

We study multivariate generalizations of the $q$-central limit theorem, a generalization of the classical central limit theorem consistent with nonextensive statistical mechanics. Two types of generalizations are addressed, more precisely the {\it direct} and {\it sequential} $q$-central limit theorems are proved. Their relevance to the asymptotic scale invariance of some specially correlated systems is studied. A $q$-analog of the classic weak convergence is introduced and its equivalence to the $q$-convergence is proved for $q>1$.

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BibTeXRIS

Sabir Umarov, Constantino Tsallis. 2007-03-20. Multivariate Generalizations of the q--Central Limit Theorem. https://arxiv.org/abs/cond-mat/0703533

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