On the eigenfunctions of the complex Ornstein-Uhlenbeck operators
Probability
2015-11-03 v3 Functional Analysis
Abstract
Starting from the 1-dimensional complex-valued Ornstein-Uhlenbeck process, we present two natural ways to imply the associated eigenfunctions of the 2-dimensional normal Ornstein-Uhlenbeck operators in the complex Hilbert space . We call the eigenfunctions Hermite-Laguerre-Ito polynomials. In addition, the Mehler summation formula for the complex process are shown.
Cite
@article{arxiv.1209.4990,
title = {On the eigenfunctions of the complex Ornstein-Uhlenbeck operators},
author = {Yong Chen and Yong Liu},
journal= {arXiv preprint arXiv:1209.4990},
year = {2015}
}
Comments
16pages