Free martingale polynomials Academic Article uri icon

abstract

  • In this paper we investigate the properties of free Sheffer systems, which are certain families of martingale polynomials with respect to the free Lvy processes. First, we classify such families that consist of orthogonal polynomials; these are the free analogs of the Meixner systems. Next, we show that the fluctuations around free convolution semigroups have as principal directions the polynomials whose derivatives are martingale polynomials. Finally, we indicate how Rota's finite operator calculus can be modified for the free context. 2003 Elsevier Science (USA). All rights reserved.

published proceedings

  • Journal of Functional Analysis

author list (cited authors)

  • Anshelevich, M.

citation count

  • 43

complete list of authors

  • Anshelevich, Michael

publication date

  • June 2003