1-Meixner Random Vectors

Aurel I. Stan () and Florin Catrina ()
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Aurel I. Stan: The Ohio State University
Florin Catrina: St. John’s University

Journal of Theoretical Probability, 2021, vol. 34, issue 4, 2033-2080

Abstract: Abstract A definition of d-dimensional n-Meixner random vectors is given first. This definition involves the commutators of their semi-quantum operators. After that we focus on the 1-Meixner random vectors and derive a system of d partial differential equations satisfied by their Laplace transform. We provide a set of necessary conditions for this system to be integrable. We use these conditions to give a complete characterization of all non-degenerate three-dimensional 1-Meixner random vectors. It must be mentioned that the three-dimensional case produces the first example in which the components of a 1-Meixner random vector cannot be reduced, via an injective linear transformation, to three independent classic Meixner random variables.

Keywords: Semi-quantum operators; Commutators; Gamma distributions; 1-Meixner random vectors; Laplace transform; 42C05; 46L53 (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s10959-020-01023-y

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