Multivariate time-space harmonic polynomials: a symbolic approach
Probability
2013-10-17 v1
Abstract
By means of a symbolic method, in this paper we introduce a new family of multivariate polynomials such that multivariate L\'evy processes can be dealt with as they were martingales. In the univariate case, this family of polynomials is known as time-space harmonic polynomials. Then, simple closed-form expressions of some multivariate classical families of polynomials are given. The main advantage of this symbolic representation is the plainness of the setting which reduces to few fundamental statements but also of its implementation in any symbolic software. The role played by cumulants is emphasized within the generalized Hermite polynomials. The new class of multivariate L\'evy-Sheffer systems is introduced.
Cite
@article{arxiv.1310.4254,
title = {Multivariate time-space harmonic polynomials: a symbolic approach},
author = {E. Di Nardo and I. Oliva},
journal= {arXiv preprint arXiv:1310.4254},
year = {2013}
}
Comments
In press