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Wick product and Clark-Ocone formula in abstract Wiener space

We explore properties of the Wick inner product of vector valued functions in the context of an abstract Wiener space (H,B). We investigate convergence of chaos expansion of the Wick product of test functions and obtain a series expansion of the Wick (ordinary) inner product of test Wienerfunctions in terms of the ordinary (Wick) inner products of their derivatives. Next, we use an extension of stochastic integral defined on the space of generalized processes to obtain a generalization of the Clark-Ocone formula involving Wiener functions that are not necessarily differentiable in the sense of Malliavin. As a framework for our investigation, we utilize the spaces of distributions and test functions introduced by Körzlioglu and Üstünel and constructed via the second quantization of an (unbounded and positive) operator on H.