2009/06/30 by B. Dybiec, Bartlomiej Dybiec, Ewa Gudowska-Nowak +1 · 15 citations
Economics, Econometrics and Finance · Physics and Astronomy · #Anomalous diffusion #Complex Systems and Time Series Analysis #Diffusion #Diffusion process #Large deviations theory #Limit (mathematics) #Limiting #Scaling #Statistical Mechanics and Entropy #Stochastic process #Theoretical and Computational Physics #cond-mat.stat-mech
paper · pdf · doi:10.1209/0295-5075/88/10003
published in Europhysics Letters (EPL) 88(1), 10003 (Institute of Physics) · 5 pages, 3 figures
arxiv created 2009/09/01 · openalex publication_date 2009/10/01 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We are discussing the 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 a truly memory-less process and the non-Markov one, we are analyzing the deviation of the survival probability from the (standard) Sparre Andersen scaling.