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Lacunarity of the zero crossings of Gaussian processes

Ogunshemi, A.; Hopcraft, K. I.; Preston, S. P.

Authors

A. Ogunshemi

K. I. Hopcraft

SIMON PRESTON simon.preston@nottingham.ac.uk
Professor of Statistics and Applied Mathematics



Abstract

A lacunarity analysis of the zero-crossings derived from Gaussian stochastic processes with oscillatory autocorrelation functions is evaluated and reveals distinct multi-scaling signatures depending on the smoothness and degree of anti-correlation of the process. These bear qualitative similarities and quantitative distinctions from an oscillatory deterministic signal and a Poisson random process both possessing the same mean interval-size between crossings. At very small and large scales compared with the correlation length of the random processes, the lacunarity is similar to the Poisson but exhibits significant departures from Poisson behaviour if there is a zero-frequency component to the process’s power-spectrum. A comparison of exact results with the gliding box technique that is frequently used to determine lacunarity demonstrates its inherent bias.

Citation

Ogunshemi, A., Hopcraft, K. I., & Preston, S. P. (2019). Lacunarity of the zero crossings of Gaussian processes. Physical Review E, 99(6), Article 062109. https://doi.org/10.1103/physreve.99.062109

Journal Article Type Article
Acceptance Date May 15, 2019
Online Publication Date Jun 5, 2019
Publication Date Jun 5, 2019
Deposit Date Jul 4, 2019
Publicly Available Date Mar 29, 2024
Journal Physical Review E
Print ISSN 2470-0045
Electronic ISSN 2470-0053
Publisher American Physical Society
Peer Reviewed Peer Reviewed
Volume 99
Issue 6
Article Number 062109
DOI https://doi.org/10.1103/physreve.99.062109
Public URL https://nottingham-repository.worktribe.com/output/2266531
Publisher URL https://journals.aps.org/pre/abstract/10.1103/PhysRevE.99.062109
Additional Information ©2019 American Physical Society

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