Wick theorems in non-Gaussian white noise calculus

The well-known Wick theorem expresses product of Gaussian fields by a sum of their normal products. In the paper, we define, first, a λ, θ-field to be a family of operators of multiplication by a λ, θ-white noise—the time derivative of the corresponding process with independent increments possessing the chaotic representation property. Special cases of such fields are the Gaussian and Poisson ones. Then, for an arbitrary λ, θ-field, we formulate and prove the Wick theorem, as well as its generalization, to the case of a product of normally ordered products of λ, θ-fields.