A modification of the Wiener process due to a Poisson random train of diffusion-enhancing pulses

Abstract

A Poisson-modified Wiener process is considered. Its conditional probability density is calculated exactly. Various forms of the evolution equation are derived for the case when the initial probability density is arbitrary. A generalization is also treated when this equation contains a term analogous to the potential energy term in the Schrodinger equation. The Green function of this equation is derived in the form of a functional integral which may be considered as a direct generalization of the Feynman-Kac integral. An application is suggested in the theory of quasiparticles with a non-parabolic dispersion law.