Noncommutative characterization of free Meixner processes

Wiktor Ejsmont (Wroclaw University of Economics and University of Wroclaw)

Abstract


In this article we give a purely noncommutative criterion for the characterization of free Meixner random variables. We prove that some families of free Meixner distributions can be described in terms of the conditional expectation, which has no classical analogue. We also show a generalization of Speicher's formula (relating moments and free cumulants) and establish a new relation in free probability.

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Pages: 1-12

Publication Date: March 24, 2013

DOI: 10.1214/ECP.v18-2356

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