English

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 L\Cnum2(μ)L_{\Cnum}^2(\mu). We call the eigenfunctions Hermite-Laguerre-Ito polynomials. In addition, the Mehler summation formula for the complex process are shown.

Keywords

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

R2 v1 2026-06-21T22:09:25.520Z