H-derivative

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In mathematics, the H-derivative is a notion of derivative in the study of abstract Wiener spaces and the Malliavin calculus.

Definition[edit]

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[disambiguation needed] of , we have .

See also[edit]

References[edit]