Forced dichotomic diffusion in a viscous media

In this paper, we study the dynamical properties of a linear system driven by a superposition of a Gaussian white noise and a symmetric Markovian dichotomic noise operating simultaneously on the system. We find exact analytical solutions for the moment generating function and for the probability distribution function. We show analytically that the system presents characteristics belonging to the nonlinear cases, such as a nonequilibrium bimodal distribution. We infer that the white Gaussian noise smooths the two characteristics Diracs delta peaks, generated by a purely dichotomic diffusion, transforming them in two smooth maxima.