Before revision:  This gives as a result an integro-differential equation, which can be solved analytically in some cases and numerically in others.
After revision:  This technique gives a dynamical insight into the evolution of the PDF, e.g., allowing the calculation of its relaxation times. Their equilibrium PDFs can also be calculated by finding its stationary solutions. This gives as a result an integro-differential equation, which can be solved analytically in some cases and numerically in others.