Free Stochastic Measures via Noncrossing Partitions
by
Michael Anshelevich
University of California, Berkeley

In the context of free probability theory, we consider multiple stochastic measures with freely independent stationary increments. Using the combinatorial machinery of the multidimensional R-transform, we calculate these measures for the free Poisson and the free compound Poisson cases. We also derive general combinatorial Itô-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.

http://front.math.ucdavis.edu/math.OA/9903084

Date received: March 22, 1999

Copyright © 1999 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cacw-11.