 Speed density of a one-dimensional diffusion

For a diffusion with generator $({\sigma }^2/2){\partial }_{xx}+b{\partial }_x$ and increasing scale function of a one-dimensional diffusion $s$, its speed density is $m=2/({\sigma }^2{s}^{\prime })$. Scale records hitting probabilities; speed records expected occupation and exit times. Multiplying scale by a positive constant divides speed by the same constant, leaving their Green-kernel product unchanged.