Wick Calculus for Vector-valued Gaussian White Noise Functionals

Based on a Gel’fand triple (N) ⊗Ɛ ⊂Γ(H) ⊗h ⊂((N) ⊗Ɛ)∗, we introduce a new notion of Wick type product of generalized Gaussian white noise functionals which is associated with a continuous bilinear mapping B : Ɛ∗ ×Ɛ∗ → Ɛ∗. 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.