Interdisciplinary Information Sciences
Online ISSN : 1347-6157
Print ISSN : 1340-9050
ISSN-L : 1340-9050
Special Issue: New Trends in Infinite Dimensional Analysis and Quantum Probability
A Generalization of the Monotonic and Boolean Independence of Algebras and Applications to Probability
Janusz WYSOCZAŃSKI
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2009 Volume 15 Issue 3 Pages 389-397

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Abstract

We present a notion of bm-independence, which generalizes the boolean and monotonic independences. The generalization is defined for partially ordered index sets. For each independence there is an analogue of the classical central limit theorem. In the case of bm-independence this depends also on the index set. Examples of such partially ordered index sets are discrete lattices in symmetric positive cones.

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© 2009 by the Graduate School of Information Sciences (GSIS), Tohoku University

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