1--Meixner random vectors
Aurel I. Stan, Florin Catrina

TL;DR
This paper introduces the concept of $d$-dimensional $n$-Meixner random vectors, derives PDEs for their Laplace transforms, and characterizes all non-degenerate three-dimensional cases, highlighting their unique non-reducibility.
Contribution
It defines $n$-Meixner random vectors using semi-quantum operators and provides a complete characterization of three-dimensional cases, revealing new structural properties.
Findings
Derived PDE system for Laplace transforms of $1$-Meixner vectors.
Established necessary conditions for PDE integrability.
Characterized all non-degenerate three-dimensional $1$-Meixner vectors.
Abstract
A definition of --dimensional --Meixner random vectors is given first. This definition involves the commutators of their semi--quantum operators. After that we will focus on the -Meixner random vectors, and derive a system of 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 --Meixner random vectors. It must be mentioned that the three--dimensional case produces the first example in which the components of a --Meixner random vector cannot be reduced, via an injective linear transformation, to three independent classic Meixner random variables.
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Taxonomy
TopicsProbabilistic and Robust Engineering Design · Mathematical Approximation and Integration · Scientific Research and Discoveries
