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
2006-01-01
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.File in questo prodotto:
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