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

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