Abstract
Using two simple examples, the continuous-time random walk as well as a two state Markov chain, the relation between generalized anomalous relaxation equations and semi-Markov processes is illustrated. This relation is then used to discuss continuous-time random statistics in a general setting, for statistics of convolution-type. Two examples are presented in some detail: the sum statistic and the maximum statistic.
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Contribution to the Topical Issue “Continuous Time Random Walk Still Trendy: Fifty-year History, Current State and Outlook”, edited by Ryszard Kutner and Jaume Masoliver.
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Scalas, E. Continuous-time statistics and generalized relaxation equations. Eur. Phys. J. B 90, 209 (2017). https://doi.org/10.1140/epjb/e2017-80311-5
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DOI: https://doi.org/10.1140/epjb/e2017-80311-5