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 A. - In: STOCHASTIC ANALYSIS AND APPLICATIONS. - ISSN 0736-2994. - STAMPA. - 24:4(2006), pp. 795-811. [10.1080/07362990600751878]
Translated Brownian motions and associated Wick products
LANCONELLI A
Investigation
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
