Bistable stochastic processes in the q-exponential family

Stochastic bistable systems whose stationary distributions belong to the q-exponential family are investigated using two approaches: (i) the Langevin model subjected to additive and quadratic multiplicative noise, and (ii) the superstatistical model. Previously, the bistable Langevin model has been analyzed under linear multiplicative noise, whereas this paper reports on quadratic multiplicative noise, which is more physically meaningful. The stationary distribution of the Langevin model under quadratic multiplicative noise, which agrees with that derived by the maximum Tsallis entropy method, is found to be qualitatively different from its counterpart under linear multiplicative noise. We also show that the stationary distribution of the superstatistical model is the same as that of the Langevin model, whereas their transient properties, described in terms of mean first passage times (MFPTs), are qualitatively different.