How to apply Novikov Theorem in Deriving Fokker-Planck Equation?

I am looking at this paper Smoluchowski diffusion equation for active Brownian swimmers, in which they describe using something called Novikov’s theorem to take correlations between a random force and a delta function that describes density. I have tried reading the references they provide, but the math is just beyond me. Has anyone encountered this or do they have a clear explanation?

From the paper:

Given a stochastic brownian processes $beta(t)$, described by a vanishing average $<beta(t)> = 0$ and correlation $<beta(t)beta(s)> =2gammadelta(t-s)$

The functional of that process $F[beta(t)]$ has the property

$$
<F[beta(t)]beta(t)> = gamma<frac{tilde{delta}F[beta(t)]}{tilde{delta}beta(t)}>
$$
Where the right hand side is the variational derivative.

They then use that theorem to get this… (moving from equations 2 to 3)

$$
-nablacdot<xi(t)delta(x-x(t))delta(varphi-varphi(t)> = D_Bnabla^2P(x,varphi,t)
$$