PreprintarXiv licencearXiv
Explicit descriptions of all 1-Meixner random vectors
Abstract
The 1-Meixner random vectors consist of d 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 $0$ in a Euclidean d-space. We provide explicit descriptions of all solutions of the system just mentioned in every dimension d.
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BibTeX
@misc{catrina2026explicit,
title = {{Explicit descriptions of all 1-Meixner random vectors}},
author = {Florin Catrina and Andrzej Derdzinski and Aurel I. Stan},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.15226},
eprint = {2610.15226},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.15226},
}
RIS
TY - UNPB
TI - Explicit descriptions of all 1-Meixner random vectors
AU - Florin Catrina
AU - Andrzej Derdzinski
AU - Aurel I. Stan
PY - 2026
DA - 2026/10/10
PB - arXiv
DO - 10.48550/arxiv.2610.15226
UR - https://arxiv.org/abs/2610.15226
AB - The 1-Meixner random vectors consist of d 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 $0$ in a Euclidean d-space. We provide explicit descriptions of all solutions of the system just mentioned in every dimension d.
ER -