After taking limit h tends to 0, how did we get that step? How did it become derivative of pij(s,t)??
Because that is by definition the derivative of pij (s,t) with respect to s. Lim(h tends to 0) ( pij(s-h,t) - pij(s,t)/(-h)) = (d/ds) (pij(s,t)) This is something analogous to what is happening in Kolomogorov forward differential equation.
