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On the difference between Malliavin derivative and Gross-Sobolev derivative

Let $W=C_0([0,1],\mathbb R^d)$ be the classical Wiener space equipped with $\mu$ the Wiener measure. If $F:W\to\mathbb R$ is a cylindrical function of the form \begin{align*} F(w)=f(W_{t_1}(w),\cdots, …
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