Onsager-Machlup Function for one dimensional nonlinear diffusion processes

Abstract

Using Ito stochastic differential equations to describe stochastic processes the Onsager-Machlup Function of a nonlinear diffusion process is calculated. It is shown that for two examples the Onsager-Machlup Function calculated directly as limit of finite dimensional probability densities agrees with the formula derived by using the Ito calculus but differs from a formula given by Graham who used the concept of Langevin equations.