Free stochastic measures via noncrossing partitions
Operator Algebras
2007-05-23 v3 Probability
Abstract
We consider free multiple stochastic measures in the combinatorial framework of the lattice of all diagonals of an n-dimensional space. In this free case, one can restrict the analysis to only the noncrossing diagonals. We give definitions of what free multiple stochastic measures are, and calculate them for the free Poisson and free compound Poisson processes. We also derive general combinatorial It\^{o}-type relationships between free stochastic measures of different orders. These allow us to calculate, for example, free Poisson-Charlier polynomials, which are the orthogonal polynomials with respect to the free Poisson measure.
Cite
@article{arxiv.math/9903084,
title = {Free stochastic measures via noncrossing partitions},
author = {Michael Anshelevich},
journal= {arXiv preprint arXiv:math/9903084},
year = {2007}
}
Comments
23 pages, AMS-LaTeX2e; statement of Proposition 3 corrected