Large deviations of time-averaged statistics for Gaussian processes
- In this paper we study the large deviations of time averaged mean square displacement (TAMSD) for Gaussian processes. The theory of large deviations is related to the exponential decay of probabilities of large fluctuations in random systems. From the mathematical point of view a given statistics satisfies the large deviation principle, if the probability that it belongs to a certain range decreases exponentially. The TAMSD is one of the main statistics used in the problem of anomalous diffusion detection. Applying the theory of generalized chi-squared distribution and sub-gamma random variables we prove the upper bound for large deviations of TAMSD for Gaussian processes. As a special case we consider fractional Brownian motion, one of the most popular models of anomalous diffusion. Moreover, we derive the upper bound for large deviations of the estimator for the anomalous diffusion exponent. (C) 2018 Elsevier B.V. All rights reserved.
Author details: | J. Gajda, Agnieszka WylomanskaORCiD, Holger KantzORCiD, Aleksei ChechkinORCiDGND, Grzegorz SikoraORCiD |
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DOI: | https://doi.org/10.1016/j.spl.2018.07.013 |
ISSN: | 0167-7152 |
ISSN: | 1879-2103 |
Title of parent work (English): | Statistics & Probability Letters |
Publisher: | Elsevier |
Place of publishing: | Amsterdam |
Publication type: | Article |
Language: | English |
Year of first publication: | 2018 |
Publication year: | 2018 |
Release date: | 2021/06/28 |
Tag: | Anomalous diffusion exponent; Fractional Brownian motion; Large deviation statistics; Sub-gamma random variable |
Volume: | 143 |
Number of pages: | 9 |
First page: | 47 |
Last Page: | 55 |
Funding institution: | NCN Maestro, Germany [2012/06/A/ST1/00258]; National Center of Science Opus, Germany [2016/21/B/ST1/00929]; Deutsche Forschungsgemeinschaft, GermanyGerman Research Foundation (DFG) [ME 1535/6-1] |
Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Physik und Astronomie |
DDC classification: | 5 Naturwissenschaften und Mathematik / 53 Physik / 530 Physik |
Peer review: | Referiert |
Publishing method: | Open Access / Green Open-Access |