Record Statistics of Continuous Time Random Walk

Details Record Statistics of Continuous Time Random Walk Record Statistics of Continuous Time Random Walk

2010-08-10

arxiv.org/abs/1008.1762v2

EPL, 94 (2011) 20003

Physics

Condensed Matter

Statistical Mechanics

5 pages, 3 figures; EPL published version

Scientific paper

10.1209/0295-5075/94/20003

The statistics of records for a time series generated by a continuous time random walk is studied, and found to be independent of the details of the jump length distribution, as long as the latter is continuous and symmetric. However, the statistics depend crucially on the nature of the waiting time distribution. The probability of finding M records within a given time duration t, for large t, has a scaling form, and the exact scaling function is obtained in terms of the one-sided Levy stable law. The mean of the ages of the records, defined as , differs from t/. The asymptotic behaviour of the shortest and the longest ages of the records are also studied.

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