Anomalous diffusion and generalized Sparre Andersen scaling. Dybiec, B. & Gudowska-Nowak, E. EPL, 2009.
doi  abstract   bibtex   
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. Copyright © 2009 EPLA.
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 title = {Anomalous diffusion and generalized Sparre Andersen scaling},
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 year = {2009},
 volume = {88},
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 abstract = {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. Copyright © 2009 EPLA.},
 bibtype = {article},
 author = {Dybiec, B. and Gudowska-Nowak, E.},
 doi = {10.1209/0295-5075/88/10003},
 journal = {EPL},
 number = {1}
}

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