The Preisach model with stochastic input as a model for aftereffect

In previous papers, we have suggested to use the Preisach model driven by stochastic inputs as a model for aftereffect. However, in these papers the stochastic inputs have been modeled by discrete time I.I.D. (independent identically distributed) random processes. Here, we further extend the aforementioned approach by modeling the stochastic inputs by continuous time diffusion processes. It is shown that the mathematical machinery of the ‘‘exit problem’’ is instrumental for calculations of time evolutions of the expected value of the output of the Preisach model.