The generalized Ornstein - Uhlenbeck process

Abstract

Langevin-like equations have been studied in the presence of arbitrary noise. The characteristic functional of the generalized Langevin process has been built up. Exact results for all cumulants are given. Particular stress has been put on the Campbell, dichotomous and radioactive decay noises. Transient relaxation, susceptibility and diffusion constants for different (noisy) media have been sketched in order to exemplify the theory. The generalized Ornstein - Uhlenbeck and Wiener processes have been completely characterized. The generalized Kubo oscillator has been worked out and all its 1-time moments have been calculated for different noise structures.