Abstract. In this paper, we developed a non-Gaussian Wick calculus based on the theory of hypecomplex systems . Using the Delsarte characters , we introduce a -Wick product, a -Hermite transform on the space of generalized functions and discuss their properties. By means of the usual properties of complex analytic functions, we proved the characterization theorem for . Moreover, we setup a framework to study the stochastic partial differential equations driven by -processes, and apply this framework to solve the -stochastic Poisson equation.

Received: April 25, 2016

Revised: July 27, 2016

Published: October 1, 2016

AMS Subject Classification: 46FXX, 30G35, 91G80

Key Words and Phrases: non-Gaussian, Wick product, Hermite transform, white noise, hypercomplex systems
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DOI: 10.12732/ijpam.v109i3.5 How to cite this paper?

Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2016
Volume: 109
Issue: 3
Pages: 539 - 556

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This work is licensed under the Creative Commons Attribution International License (CC BY).

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