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Clark-Ocone Formula for Generalized Functionals of Discrete-Time Normal Noises
oleh: Caishi Wang, Shuai Lin, Ailing Huang
| Format: | Article |
|---|---|
| Diterbitkan: | Hindawi Limited 2018-01-01 |
Deskripsi
The Clark-Ocone formula in the theory of discrete-time chaotic calculus holds only for square integrable functionals of discrete-time normal noises. In this paper, we aim at extending this formula to generalized functionals of discrete-time normal noises. Let Z be a discrete-time normal noise that has the chaotic representation property. We first prove a result concerning the regularity of generalized functionals of Z. Then, we use the Fock transform to define some fundamental operators on generalized functionals of Z and apply the abovementioned regularity result to prove the continuity of these operators. Finally, we establish the Clark-Ocone formula for generalized functionals of Z and show its application results, which include the covariant identity result and the variant upper bound result for generalized functionals of Z.