We will now derive the Fokker-Planck equation. We start from the ESKC equation
$$ W(\mathbf{x},t|\mathbf{x}_0,t_0) = \int_{-\infty}^{\infty} W(\mathbf{x},t|\mathbf{x}',t')W(\mathbf{x}',t'|\mathbf{x}_0,t_0)d\mathbf{x}'. $$Define \( s=t'-t_0 \), \( \tau=t-t' \) and \( t-t_0=s+\tau \). We have then
$$ W(\mathbf{x},s+\tau|\mathbf{x}_0) = \int_{-\infty}^{\infty} W(\mathbf{x},\tau|\mathbf{x}')W(\mathbf{x}',s|\mathbf{x}_0)d\mathbf{x}'. $$