Importance sampling, Fokker-Planck and Langevin equations

We say thus that $\mathbf{x}$ changes only by a small amount in the time interval $\tau$. This means that we can make a Taylor expansion in terms of $\xi$, that is we expand

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

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