Restoring ergodicity of stochastically reset anomalous-diffusion processes

Anomalous diffusion and ergodicity breaking in heterogeneous diffusion processes

Andrey G. Cherstvy, Aleksei V. Chechkin, 3 and Ralf Metzler 4 Institute for Physics & Astronomy, University of Potsdam, 14476 Potsdam-Golm, Germany Akhiezer Institute for Theoretical Physics, Kharkov Institute of Physics and Technology, Kharkov 61108, Ukraine Max-Planck Institute for the Physics of Complex Systems, Nöthnitzer Straße 38, 01187 Dresden, Germany Department of Physics, Tampere Univ...

Ergodicity testing for anomalous diffusion: small sample statistics.

The analysis of trajectories recorded in experiments often requires calculating time averages instead of ensemble averages. According to the Boltzmann hypothesis, they are equivalent only under the assumption of ergodicity. In this paper, we implement tools that allow to study ergodic properties. This analysis is conducted in two classes of anomalous diffusion processes: fractional Brownian mot...

Ergodicity of Langevin Processes with Degenerate Diffusion in Momentums

This paper introduces a geometric method for proving ergodicity of degenerate noise driven stochastic processes. The driving noise is assumed to be an arbitrary Levy process with non-degenerate diffusion component (but that may be applied to a single degree of freedom of the system). The geometric conditions are the approximate controllability of the process the fact that there exists a point i...

Anomalous Diffusion, Stable Processes, and Generalised Functions

Anomalous diffusion, stable processes, and generalized functions.

The evolution equations in real space and time corresponding to a class of anomalous diffusion processes are examined. As special cases, evolution equations corresponding to stable processes are derived using the theory of generalized functions, recovering some known results differently interpreted, and an evolution law for stable processes of order unity.