First-Passage Times for Random Diffusivity Models

Random diffusivity models have gained more and more interest over the last decade as they allow for a rather simple mathematical framework to introduce different kinds of system heterogeneity in the description of diffusion dynamics. In this chapter, we briefly recall the general properties of such models and then provide a detailed description of their first-passage time properties. We start by showing how, through the subordination approach, a formal solution of any first-passage time problem can be defined, starting from the analogous solution of standard Brownian diffusion. We present results on the first-passage time density obtained directly from the solution of the associated Fokker-Planck equation. Eventually, we provide applications to special cases and focus on the statistical properties and asymptotic behaviors of one diffusing diffusivity model. A comparison of such a study with the results from standard (homogeneous) Brownian diffusion is also discussed. To conclude, we highlight possible future directions.