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New characterization of two-state normal distribution

Wiktor Ejsmont

Department of Mathematics and Cybernetics, Wrocław University of Economics, Address: Komandorska 118/120, 53-345 Wrocław, Poland

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https://doi.org/10.1142/S0219025714500192Cited by:2 (Source: Crossref)

Abstract

In this paper we give a purely noncommutative criterion for the characterization of two-state normal distribution. We prove that families of two-state normal distribution can be described by relations which is similar to the conditional expectation in free probability, but has no classical analogue. We also show a generalization of Bożejko, Leinert and Speichers formula from Ref. 10 (relating moments and noncommutative cumulants).

Keywords:

AMSC: 22E46, 53C35, 57S20

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