H-derivative
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This article may be too technical for most readers to understand.(June 2012) |
In mathematics, the H-derivative is a notion of derivative in the study of abstract Wiener spaces and the Malliavin calculus.
Definition
Let be an abstract Wiener space, and suppose that is differentiable. Then the Fréchet derivative is a map
- ;
i.e., for , is an element of , the dual space to .
Therefore, define the -derivative at by
- ,
a continuous linear map on .
Define the -gradient by
- .
That is, if denotes the adjoint of , we have .
See also
References
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