Orthogonal polynomial solutions of the Fokker-Planck equation

Abstract

We have tabulated the form of the coefficientsg1(x) andg2(x) as well as the boundary values [a, b] of the Fokker-Planck equation $$\frac{{\partial P(x, t)}}{{\partial t}} = - \frac{\partial }{{\partial x}}[g_1 (x)P(x, t)] + \frac{{\partial ^2 }}{{\partial x^2 }}[g_2 (x)P(x, t)],a \leqslant x \leqslant b$$ for which the solution can be written as an eigenfunction expansion in the classical orthogonal polynomials. We also discuss the problem of finding solutions in terms of the discrete classical polynomials for the differential difference equations of stochastic processes.