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arxiv: 1209.4990 · v3 · pith:AMRH6VQDnew · submitted 2012-09-22 · 🧮 math.PR · math.FA

On the eigenfunctions of the complex Ornstein-Uhlenbeck operators

classification 🧮 math.PR math.FA
keywords complexeigenfunctionsornstein-uhlenbeckdimensionaloperatorsprocessadditionassociated
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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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