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Embedding the Abstract Wiener Space in a Probability Space

✍ Scribed by A.S. Üstünel; M. Zakai

Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
160 KB
Volume
171
Category
Article
ISSN
0022-1236

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✦ Synopsis

In the first part, of this paper it is pointed out that for certain applications of the stochastic calculus of variations it is useful to replace the classical domain of definition the Wiener space with a general probability space in which the Wiener space is embedded. This yields a certain conditional Malliavin calculus'' and is applicable to signal'' and ``noise'' problems. In a somewhat analogous way, it is pointed out in the second part of the paper that formulating the Ito^calculus in a setup of an abstract Wiener space embedded in a general probability space endowed with a filtration has certain useful applications. In particular it enables the formulation and derivation of a dimension-free form of the Girsanov theorem as well as a dimension free form of the representation of L p -Wiener functionals as Ito^integrals.

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