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On the eigenfunctions of the complex Ornstein-Uhlenbeck operators
Published 22 Sep 2012 in math.PR and math.FA | (1209.4990v3)
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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