Multivariate Generalizations of the q--Central Limit Theorem

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 $q>1$.

15 pages

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• A generalization of the central limit theorem consistent with nonextensive statistical mechanics
• Tsallis non-extensive statistics, intermittent turbulence, SOC and chaos in the solar plasma. Part one: Sunspot dynamics
• On the role of ergodicity and mixing in the central limit theorem for Casati-Prosen triangle map variables
• Newton based Stochastic Optimization using q-Gaussian Smoothed Functional Algorithms