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Corpus ID: 220280160

Limit Forms of the Distribution of the Number of Renewals

@article{Burov2020LimitFO,
title={Limit Forms of the Distribution of the Number of Renewals},
author={S. Burov},
journal={arXiv: Statistical Mechanics},
year={2020}
}

In this work the asymptotic properties of $Q_t(N)$ ,the probability of the number of renewals ($N$), that occur during time $t$ are explored. While the forms of the distribution at very long times, i.e. $t\to\infty$, are very well known and are related to the Gaussian Central Limit Theorem or the Levy stable laws, the alternative limit of large number of renewals, i.e. $N\to\infty$, is much less noted. We address this limit of large $N$ and find that it attains a universal form that solely… Expand

The analysis shows how the large-deviation properties can be efficiently used as a simple yet effective routine test to reject the BM hypothesis and unveil relevant information on statistical properties such as ergodicity breaking and short-time correlations.Expand