The input dependent Preisach model with stochastic input as a model for aftereffect

In a previous work, it has been suggested to use the Preisach model driven by stochastic inputs as a model for aftereffect. Here, we further extend this approach by employing the more accurate nonlinear input dependent Preisach model. The time evolution of the expected value of the output (magnetization) is derived in terms of the stochastic description of the input. 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 nonlinear input dependent Preisach model