31 citations · 44 across the 4 of their papers we have counts for
9 papers
Zimmermann Type Cancellation in the Free Faa di Bruno Algebra
Michael Anshelevich, Edward G. Effros, Mihai Popa
The N-variable Hopf algebra introduced by Brouder, Fabretti, and Krattenaler (BFK) in the context of non-commutative Lagrange inversion can be identified with the inverse of the in…
Appell polynomials and their relatives
Michael Anshelevich
This paper summarizes some known results about Appell polynomials and investigates their various analogs. The primary of these are the free Appell polynomials. In the multivariate…
q-Levy processes
Michael Anshelevich
We continue the investigation of the Levy processes on a q-deformed full Fock space started in a previous paper. First, we show that the vacuum vector is cyclic and separating for…
Linearization coefficients for orthogonal polynomials using stochastic processes
Michael Anshelevich
Given a basis for a polynomial ring, the coefficients in the expansion of a product of some of its elements in terms of this basis are called linearization coefficients. These coef…
Free martingale polynomials
Michael Anshelevich
In this paper we investigate the properties of the free Sheffer systems, which are certain families of martingale polynomials with respect to the free Levy processes. First, we cla…
Ito formula for free stochastic integrals
Michael Anshelevich
The objects under investigation are the stochastic integrals with respect to free Levy processes. We define such integrals for square-integrable integrands, as well as for a certai…