Acta Mathematicae Applicatae Sinica, English Series

, Volume 25, Issue 3, pp 399–414

Wick calculus for nonlinear Gaussian functionals


DOI: 10.1007/s10255-008-8808-0

Cite this article as:
Hu, Yz. & Yan, Ja. Acta Math. Appl. Sin. Engl. Ser. (2009) 25: 399. doi:10.1007/s10255-008-8808-0


This paper surveys some results on Wick product and Wick renormalization. The framework is the abstract Wiener space. Some known results on Wick product and Wick renormalization in the white noise analysis framework are presented for classical random variables. Some conditions are described for random variables whose Wick product or whose renormalization are integrable random variables. Relevant results on multiple Wiener integrals, second quantization operator, Malliavin calculus and their relations with the Wick product and Wick renormalization are also briefly presented. A useful tool for Wick product is the S-transform which is also described without the introduction of generalized random variables.


Malliavin calculusmultiple integralchaos decompositionWick productWick renormalization

2000 MR Subject Classification


Copyright information

© Institute of Applied Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences and Springer-Verlag GmbH 2009

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of KansasLawrenceUSA
  2. 2.Academy of Mathematics and Systems ScienceChinese Academy of SciencesBeijingChina