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On a nonsymmetric Ornstein-Uhlenbeck semigroup and its generator

Research paper by Yong Chen

Indexed on: 25 Nov '13Published on: 25 Nov '13Published in: Mathematics - Probability



Abstract

If we add a simple rotation term to both the Ornstein-Uhlenbeck semigroup and the definition of the H-derivative, then analogue to the classical Malliavin calculus on the real Wiener space [I. Shigekawa, Stochastic analysis, 2004], we get a normal but nonsymmetric Ornstein-Uhlenbeck operator $L$ on the complex Wiener space. The eigenfunctions of the operator $L$ are given. In addition, the hypercontractivity for the nonsymmetric Ornstein-Uhlenbeck semigroup is shown.