Gaussian integration by parts: $\mathbb E[U\,G(V)]=\sum_j \mathrm{Cov}(U,V_j)\,\mathbb E[\partial_j G(V)]$ for jointly Gaussian $(U,V)$, $U$ centered, $G\in C^1_b$

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Gaussian integration by parts: $\mathbb E[U\,G(V)]=\sum_j \mathrm{Cov}(U,V_j)\,\mathbb E[\partial_j G(V)]$ for jointly Gaussian $(U,V)$, $U$ centered, $G\in C^1_b$ · Prove2Me