Skorokhod Integral
The Skorokhod integral operator which is conventionally denoted δ is defined as the adjoint of the Malliavin derivative thus for u in the domain of the operator which is a subset of, for F in the domain of the Malliavin derivative, we require
where the inner product is that on viz
The existence of this adjoint follows from the Riesz representation theorem for linear operators on Hilbert spaces.
It can be shown that if u is adapted then
where the integral is to be understood in the Itô sense. Thus this provides a method of extending the Itô integral to non adapted integrands.
Read more about this topic: Malliavin Calculus
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