Stochastic processes driven by dichotomous Markov noise: Some exact dynamical results

Stochastic processes defined by a general Langevin equation of motion where the noise is the non-Gaussian dichotomous Markov noise are studied. A non-Fokker–Planck master differential equation is deduced for the probability density of these processes. Two different models are exactly solved. In the second one, a nonequilibrium bimodal distribution induced by the noise is observed for a critical value of its correlation time. Critical slowing down does not appear in this point but in another one.