Novikov's theorem
= Novikov's theorem
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For a centered <Gaussian random field> $W$ with covariance $C$ and a sufficiently regular functional $F[W]$, the Furutsu--Novikov formula is the functional <integration by parts> identity
$$
\mathbb E[W(x)F[W]]
=\int C(x,y)\mathbb E\left[\frac{\delta F}{\delta W(y)}\right]dy.
$$
It closes moment equations for systems driven multiplicatively by Gaussian fluctuations.
= Furutsu–Novikov formula
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{synonym}