Study of stochastic resonance in processes with multiplicative noise by means of first passage times simulation

We study the response to weak periodic stimuli of a class of one-dimensional diffusion processes with multiplicative noise. Since an indicator of stochastic resonant behavior is the first passage time distribution, i.e. the distribution of the random times at which the process first reaches a given boundary, after recalling the required theoretical background we evaluate such distribution in the cases of interest by means of the quoted simulation technique. We expose and discuss the results obtained in a series of exemplification cases, hinting to the arising of the stochastic resonance phenomenon for the considered processes.