New characterization of two-state normal distribution

Abstract

In this article 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 Bozejko, Leinert and Speicher's formula (relating moments and noncommutative cumulants).

19 pages, 2 figures, accepted for publication by Infinite Dimensional Analysis, Quantum Probability and Related Topics

References in corpus (2)

• On a class of free Levy laws related to a regression problem
• Appell polynomials and their relatives II. Boolean theory

Cited by in corpus (1)

• Convolution, subordination and characterization problems in noncommutative probability