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 gamma-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 gamma-Wick products.

Translated Brownian motions and associated Wick products

LANCONELLI, ALBERTO
2006

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 gamma-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 gamma-Wick products.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11586/16780
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