In this paper, we developed a non-Gaussian Wick calculus based on the theory of hypecomplex systems L1(Q, dm(x)). Using the Delsarte characters n(x), we introduce a -Wick product, a -Hermite transform on the space of generalized functions H -q and discuss their properties. By means of the usual properties of complex analytic functions, we proved the characterization theorem for H -q . Moreover, we setup a framework to study the stochastic partial differential equations driven by H -q -processes, and apply this framework to solve the -stochastic Poisson equation.
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Hyder et al. (2016) studied this question.