A unifying approach to first-passage time distributions in diffusing diffusivity and switching diffusion models

We propose a unifying theoretical framework for the analysis of first-passage time distributions in two important classes of stochastic processes in which the diffusivity of a particle evolves randomly in time. In the first class of 'diffusing diffusivity' models, the diffusivity changes continuously via a prescribed stochastic equation. In turn, the diffusivity switches randomly between discrete values in the second class of 'switching diffusion' models. For both cases, we derive exact formulas for the probability density function of the first-passage time and quantify the impact of the diffusivity dynamics via the moment-generating function of the integrated diffusivity.