Anomalous diffusion and generalized Sparre-Andersen scaling

Abstract

We are discussing long-time, scaling limit for the anomalous diffusion composed of the subordinated Lévy-Wiener process. The limiting anomalous diffusion is in general non-Markov, even in the regime, where ensemble averages of a mean-square displacement or quantiles representing the group spread of the distribution follow the scaling characteristic for an ordinary stochastic diffusion. To discriminate between truly memory-less process and the non-Markov one, we are analyzing deviation of the survival probability from the (standard) Sparre-Andersen scaling.

5 pages, 3 figures

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• On subdiffusive continuous time random walks with stochastic resetting
• Paradoxical diffusion: Discriminating between normal and anomalous random walks
• Sparre-Andersen theorem with spatiotemporal correlations
• Subdiffusion equation with fractional Caputo time derivative with respect to another function in modeling transition from ordinary subdiffusion to superdiffusion
• Stationary states in 2D systems driven by bi-variate Lévy noises
• Escape from the potential well: competition between long jumps and long waiting times
• Optimization of escape kinetics by reflecting and resetting
• Stochastic kinetics under combined action of two noise sources