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Contents of PMS, Vol. 41, Fasc. 2,
pages 283 - 302
DOI: 10.37190/0208-4147.41.2.5
Published online 11.8.2021
 

Wick calculus for vector-valued Gaussian white noise functionals

U. C. Ji
P. C. Ma

Abstract:

Based on a Gel’fand triple (N)⊗E⊂Γ(H)⊗h⊂((N)⊗E)∗, we introduce a new notion of Wick type product of generalized Gaussian white noise functionals which is associated with a continuous bilinear mapping B:E∗×E∗→E∗. Then we study Wick type differential equations for vector-valued generalized Gaussian white noise functionals and, as a simple application, we study Wick type differential equations for matrix-valued generalized Gaussian white noise functionals. For our purposes, we make a systematic study of equicontinuity of the left and right Wick type multiplication operators.

2010 AMS Mathematics Subject Classification: Primary 60H40; Secondary 46F25, 46A11.

Keywords and phrases: white noise theory, Gaussian white noise functional, Wick product, equicontinuous, Wick type differential equation.

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