Ocone formula for vector valued random variables in abstract Wiener space
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چکیده
The classical representation of random variables as the Itô integral of nonanticipative integrands is extended to include Banach space valued random variables on an abstract Wiener space equipped with a filtration induced by a resolution of the identity on the Cameron–Martin space. The Itô integral is replaced in this case by an extension of the divergence to random operators, and the operators involved in the representation are adapted with respect to this filtration in a suitably defined sense.
منابع مشابه
The Clark–ocone Formula for Vector Valued Random Variables in Abstract Wiener Space
Erratum to " The Clark-Ocone formula for vector valued random variables in abstract Wiener space " , Jour. In this paper we considered the extension of the Clark-Ocone formula for a random variable defined on an abstract Wiener space (W, H, µ) and taking values in a Banach space (denoted there either B or Y). The main result appears in Theorem 3.4. Unfortunately, as first pointed out to us by J...
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تاریخ انتشار 2004