Manifolds of equivalent path integral solutions of the Fokker-Planck equation

Abstract

Path integral solutions of the multi-dimensional Fokker-Planck equation with variable dependent diffusion coefficients are deduced in a simple and exact manner. We show that the Onsager-Machlup function is not defined uniquely but is definable only together with the discretization prescription and the measure in the functional space. We present wide classes of mathematical equivalent path integral representations characterized by nonlinear variable transformationsv(q′, q) and the coefficientsαK of a linear combination, all giving exactly the same solution of the Fokker-Planck equation.