Quantum Decomposition Associated with the q-Deformed Lévy–Meixner White Noise

Abstract

In this paper we start with a new detailed construction of the one-mode type q-Lévy-Meixner Fock space [Formula: see text] which serves to obtain the quantum decomposition associated with the q-deformed Lévy-Meixner white noise processes. More precisely, based on the notion of quantum decomposition and the orthogonalization of polynomials of noncommutative q-Lévy-Meixner white noise [Formula: see text], we study the chaos property of the noncommutative L2-space with respect to the vacuum expectation τ. Next, we determine the distribution of the q-Lévy-Meixner operator J(χD) = ⟨ω, χD⟩ and as a consequence we give some useful properties of the q-Lévy-Meixner white noise process.