Free martingale polynomials
组合数学
2007-05-23 v1 经典分析与常微分方程
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摘要
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 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.
引用
@article{arxiv.math/0112194,
title = {Free martingale polynomials},
author = {Michael Anshelevich},
journal= {arXiv preprint arXiv:math/0112194},
year = {2007}
}
备注
AMS-LaTeX with Times fonts; 25 pages