Fokker-Planck Equation for Several Variables; Methods of Solution

Abstract

In this chapter we discuss methods of solution for the Fokker-Planck equation (4.94a, 95) for time-independent drift and diffusion coefficients, i.e., for

$$ \partial W/\partial t = {L_{FP}}W = \partial {S_i}/\partial {x_i}, $$

(6.1)

$$ {L_{FP}} = - \frac{\partial }{{\partial {x_i}}}{D_i}(\{ x\} ) + \frac{{{\partial ^2}}}{{\partial {x_i}\partial {x_j}}}{D_{ij}}(\{ x\} ). $$

(6.2)

(With the exception of Sect. 6.6.5 the summation convention for Latin indices is used in this chapter.)