Importance sampling, Fokker-Planck and Langevin equations

We can then rewrite the ESKC equation as

$$\frac{\partial W}{\partial s}\tau=-W(\mathbf{x},s|\mathbf{x}_0)+ \sum_{n=0}^{\infty}\frac{(-\xi)^n}{n!}\frac{\partial^n}{\partial x^n} \left[W(\mathbf{x},s|\mathbf{x}_0)\int_{-\infty}^{\infty} \xi^nW(\mathbf{x}+\xi,\tau|\mathbf{x})d\xi\right].$$

We have neglected higher powers of $\tau$ and have used that for $n=0$ we get simply $W(\mathbf{x},s|\mathbf{x}_0)$ due to normalization.

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