On the eigenfunctions of the complex Ornstein–Uhlenbeck operators
On the eigenfunctions of the complex Ornstein–Uhlenbeck operators
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DOI：
10.1215/21562261-2693451
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发表时间：
2012-09
影响因子：
0.6
通讯作者：
Yong Chen;Y. Liu
中科院分区：
文献类型：
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作者：
Yong Chen;Y. Liu
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.
