Explicit path integration in a Rayleigh diffusion process

Abstract

In this paper, we perform an explicit path integration to obtain the conditional probability density in a Rayleigh diffusion process. This stochastic process is often used to model the fluctuations of the amplitude of an optical field. The path integral approach is motivated by the close analogy between the Feynman kernel and the conditional probability density and by the possibility of employing the analytic techniques of path integration in quantum mechanics to stochastic processes. Moreover, while it is generally not possible to obtain closed form analytic solutions, the Rayleigh diffusion process adds to the list of completely path integrable stochastic processes.