We derive some characteristic properties of the convolution operator acting on white noise
functions and prove that the convolution product of white noise distributions coincides with …

We aim at characterizing generalized functionals of discrete‐time normal martingales. Let
M=(M n) n∈ N be a discrete‐time normal martingale that has the chaotic representation …

In this work, we employ a biorthogonal approach to construct the infinite-dimensional
Fractional Pascal measure μ σ (α), 0< α≤ 1, defined on the tempered distributions space …

Using a biorthogonal technique (Appell system), the foremost aim of this study is to develop
and highlight specific aspects of a new polynomial sequence known as Fractional …

In this article, we aim at characterizing operators acting on functionals of discrete-time
normal martingales. Let be a discrete-time normal martingale that has the chaotic …

We construct an infinite dimensional analysis with respect to non-Gaussian measures of
fractional Gamma type which we call fractional Gamma noise measures. It turns out that the …

Consider the Lévy–Meixner one-mode interacting Fock space {Γ LM,〈⋅,⋅〉 LM}. Inspired by
a derivative formula appearing in〈⋅,⋅〉 LM, we define scalar products〈⋅,⋅〉 LM, n in …

By using a unitary isomorphism UP between the interacting Fock space FP (H) and the
Pascal white noise space L 2 (S′, Λ P), we define a quantum Pascal white noise WP (t) and …

Let M be a discrete-time normal martingale that has the chaotic representation property.
Then, from the space of square integrable functionals of M, one can construct generalized …

In this paper, a characterization theorem for the S‐transform of infinite dimensional
distributions of noncommutative white noise corresponding to the (p, q)‐deformed quantum …