When $\tau \rightarrow 0$ we assume that $\langle [\Delta x(\tau)]^n\rangle \rightarrow 0$ more rapidly than $\tau$ itself if $n > 2$. When $\tau$ is much larger than the standard correlation time of system then $M_n$ for $n > 2$ can normally be neglected. This means that fluctuations become negligible at large time scales.

If we neglect such terms we can rewrite the ESKC equation as

$$\frac{\partial W(\mathbf{x},s|\mathbf{x}_0)}{\partial s}= -\frac{\partial M_1W(\mathbf{x},s|\mathbf{x}_0)}{\partial x}+ \frac{1}{2}\frac{\partial^2 M_2W(\mathbf{x},s|\mathbf{x}_0)}{\partial x^2}.$$