Hopf-algebraic deformations of products and Wick polynomials
Probability
2021-01-12 v3
Abstract
We present an approach to classical definitions and results on cumulant--moment relations and Wick polynomials based on extensive use of convolution products of linear functionals on a coalgebra. This allows, in particular, to understand the construction of Wick polynomials as the result of a Hopf algebra deformation under the action of linear automorphisms induced by multivariate moments associated to an arbitrary family of random variables with moments of all orders. We also generalise the notion of deformed product in order to discuss how these ideas appear in the recent theory of regularity structures.
Keywords
Cite
@article{arxiv.1710.00735,
title = {Hopf-algebraic deformations of products and Wick polynomials},
author = {Kurusch Ebrahimi-Fard and Frédéric Patras and Nikolas Tapia and Lorenzo Zambotti},
journal= {arXiv preprint arXiv:1710.00735},
year = {2021}
}
Comments
Revised and improved Section 9. 29 pages