Interconnection between Wick multiplication and integration on spaces of nonregular generalized functions in the Levy white noise analysis

N. A. Kachanovsky, T. Kachanovska

Abstract


We deal with spaces of nonregular generalized functions in the Levy white noise analysis, which are constructed using Lytvynov's generalization of a chaotic representation property. Our aim is to describe a relationship between Wick multiplication and integration on these spaces. More exactly, we show that when employing the Wick multiplication, it is possible to take a time-independent multiplier out of the sign of an extended stochastic integral;establish an analog of this result for a Pettis integral (a weak integral);and prove a theorem about a representation of the extended stochastic integral via the Pettis integral from the Wick product of the original integrand by a Levy white noise. As examples of an application of our results, we consider some stochastic equations with Wick type nonlinearities.


Keywords


Levy process, extended stochastic integral, Pettis integral, Wick product

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