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arXiv · 1209.4990

On the eigenfunctions of the complex Ornstein-Uhlenbeck operators

Yong Chen·Yong Liu
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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 $L_{\Cnum}^2(\mu)$. We call the eigenfunctions Hermite-Laguerre-Ito polynomials. In addition, the Mehler summation formula for the complex process are shown.

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Yong Chen, Yong Liu. 2012-09-22. On the eigenfunctions of the complex Ornstein-Uhlenbeck operators. https://doi.org/10.1215/21562261-2693451

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