On the 1-dimensional complex Ornstein-Uhlenbeck operator

2017/04/21 by Yong Chen, Chen, Yong
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #FOS: Mathematics #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations #Probability (math.PR)

paper · pdf · doi:10.48550/arxiv.1704.06583

openalex publication_date 2017/04/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that for any fixed θ∈(-\fracπ2, 0)∪ (0, \fracπ2), the 1-dimensional complex Ornstein-Uhlenbeck operator L_θ= 4cosθ\frac∂²∂ z∂ z-e^\miθ z (∂)/(∂ z)-e^-\miθz \frac∂∂ z, is a normal (but nonsymmetric) diffusion operator.

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