Affiliation:
1. Institute of Mathematics, National Academy of Sciences of Ukraine, 3, Tereschenkivska street, Kyiv, 01601, Ukraine
Abstract
Using a general approach that covers the cases of Gaussian, Poissonian, Gamma, Pascal and Meixner measures, we consider an extended stochastic integral and construct elements of a Wick calculus on parametrized Kondratiev-type spaces of generalized functions; consider the interconnection between the extended stochastic integration and the Wick calculus; and give an example of a stochastic equation with a Wick-type nonlinearity. The main results consist of studying the properties of the extended (Skorohod) stichastic integral subject to the particular spaces under consideration; and of studying the properties of a Wick product and Wick versions of holomorphic functions on the parametrized Kondratiev-type spaces. These results are necessary, in particular, in order to describe properties of solutions of normally ordered white noise equations in the "Meixner analysis".
Publisher
World Scientific Pub Co Pte Lt
Subject
Applied Mathematics,Mathematical Physics,Statistics and Probability,Statistical and Nonlinear Physics
Cited by
4 articles.
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