A sequence solution to the Fokker-Planck equation

In this paper a new approach to nonlinear system analysis based on the Fokker-Planck equation is developed. The development begins as a modification of the parametrix method of partial differential equation theory and provides a sequence solution to the multidimensional time-varying Fokker-Planck equation. This sequence is simplified for the case where only a steady-state solution or a solution for the variance of a particular combination of states is desired. Equations are presented in a form suitable for obtaining numerical results using a digital computer. This method is cast in a rather general mathematical framework and can provide useful results for a variety of problems. It is applied to the special case of phase-locked frequency demodulation, and curves of frequency tracking error are presented. Even though the rate of convergence of the sequence is not established in general, these numerical results prove the usefulness of the method for this special case and suggest a far greater range of usefulness.