Explicit descriptions of all 1-Meixner random vectors
Florin Catrina, Andrzej Derdzinski, Aurel I. Stan
Source abstract
The 1-Meixner random vectors consist of real-valued random variables, having finite moments of all orders, for which the commutators between their joint semi-quantum operators and the multiplication operators that they generate are linear combinations of these multiplication operators and the identity operator. This property of random variables imposes a system of first-order partial differential equations on their joint Laplace transform on a neighborhood of in a Euclidean -space. We provide explicit descriptions of all solutions of the system just mentioned in every dimension .
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