Asymptotic degeneracy and subdiffusivity

Abstract

The time-changing of processes by inverse subordinators is widely studied in the literature as models of subdiffusion driven by sporadic trapping. We reveal that increments of such subdiffusion processes may exhibit asymptotic degeneracy depending on the underlying stochastic temporal progression. Various surprising aspects of time-changed processes are discussed in light of asymptotic degeneracy, including diffusive dynamics and optimal inference. We also motivate asymptotic degeneracy as an important criterion for determining appropriateness of such processes for modelling real-world phenomena.