Ergodic properties of Lévy flights coexisting with subdiffusion and related models

We analyze ergodic properties of two different stationary processes resulting from a combination of Lévy flights and subdiffusion. The first one comes from the Lamperti transformation of subordinated γ-stable process. The second one is a sequence of increments of subordinated Lévy process. We prove that both processes are mixing and ergodic. We also study increments and the Lamperti transformation of time-changed fractional Brownian motion. It appears that these models of anomalous diffusion are also ergodic and mixing. We believe that the derived results will help to verify ergodicity in single particle tracking experiments.