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

    In this paper we start with a new detailed construction of the one-mode type q-Lévy-Meixner Fock space LM(q)() 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 ω(t):=bt*+c2bt+βbt*bt2+γbt*bt+c1I, 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 JD) = ⟨ω, χD⟩ and as a consequence we give some useful properties of the q-Lévy-Meixner white noise process.