Some Norm Inequalities for Gaussian Wick Products |
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| Authors: | Alberto Lanconelli Aurel I. Stan |
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| Affiliation: | 1. Dipartimento di Matematica , Universita’ degli Studi di Bari , Bari, Italia lanconelli@dm.uniba.it;3. Department of Mathematics , Ohio State University at Marion , Marion, Ohio, USA |
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| Abstract: | We provide several inequalities for the ? q (𝒫)-norm of the Wick product of random variables. These estimates are based on a Jensen's type inequality for the Wick multiplication, which we derive via a positivity argument. As an application we study a certain type of anticipating stochastic differential equation whose solution is shown to be an element of ? q (𝒫) for some q ≥ 1. |
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| Keywords: | Jensen's inequality Second quantization operator Stochastic differential equations Wick product |
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