Translated Brownian Motions and Associated Wick Products |
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| Authors: | Alberto Lanconelli |
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| Affiliation: | 1. CMAF , University of Lisbon , Lisbon, Portugal;2. Department of Mathematics , University of Pavia , Pavia, Italy lanconelli@ptmat.fc.ul.pt |
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| Abstract: | Abstract The concept of Wick product is strongly related to the underlying Brownian motion we have fixed on the probability space. Via the Girsanov's theorem we construct a family of new Brownian motions, obtained as translations of the original one, and to each of them we associate a Wick product. This produces a family of Wick products, named γ-Wick products, parameterized by the performed translations. We aim to describe this family of products. We also define a new family of stochastic integrals, which are related in a natural way to the γ-Wick products. |
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| Keywords: | Girsanov's theorem Stochastic differential equations Wick product |
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