3 citations · 7 across the 10 of their papers we have counts for
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Explicit descriptions of all 1-Meixner random vectors
Florin Catrina, Andrzej Derdzinski, Aurel I. Stan
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…
Meixner random variables and their quantum operators
Nobuaki Obata, Aurel I. Stan, Hiroaki Yoshida
We find the position-momentum decomposition of the quantum operators of the classic Meixner random variables. The position-momentum decomposition involves translation operators, wh…
1--Meixner random vectors
Aurel I. Stan, Florin Catrina
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…
A sharp interpolation between the Hölder and Gaussian Young inequalities
Paolo Da Pelo, Alberto Lanconelli, Aurel I. Stan
We prove a very general sharp inequality of the Hölder--Young--type for functions defined on infinite dimensional Gaussian spaces. We begin by considering a family of commutative p…
A note on a local limit theorem for Wiener space valued random variables
Alberto Lanconelli, Aurel Iulian Stan
We prove a local limit theorem, i.e. a central limit theorem for densities, for a sequence of independent and identically distributed random variables taking values on an abstract…
An extension of the Beckner's type Poincaré inequality to convolution measures on abstract Wiener spaces
Paolo Da Pelo, Alberto Lanconelli, Aurel I. Stan
We generalize the Beckner's type Poincaré inequality \cite{Beckner} to a large class of probability measures on an abstract Wiener space of the form , where is the ref…