In mathematics, the Malliavin derivative is a notion of derivative in the Malliavin calculus. Intuitively, it is the notion of derivative appropriate to paths in classical Wiener space, which are "usually" not differentiable in the usual sense.
By the Sobolev embedding theorem, . Let
denote the inclusion map.
Then the Malliavin derivative is defined by
The Skorokhod integral is defined to be the adjoint of the Malliavin derivative: