Wick calculus for vector-valued gaussian white noise functionals

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 map-ping 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.