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Zero-crossing statistics for non-Markovian time series
Umeå University, Faculty of Science and Technology, Department of Physics. (Integrated Science Lab)
Umeå University, Faculty of Science and Technology, Department of Physics. (Integrated Science Lab)
2018 (English)In: Physical review. E, ISSN 2470-0045, E-ISSN 2470-0053, Vol. 97, no 3, article id 032114Article in journal (Refereed) Published
Abstract [en]

In applications spanning from image analysis and speech recognition to energy dissipation in turbulence and time-to failure of fatigued materials, researchers and engineers want to calculate how often a stochastic observable crosses a specific level, such as zero. At first glance this problem looks simple, but it is in fact theoretically very challenging, and therefore few exact results exist. One exception is the celebrated Rice formula that gives the mean number of zero crossings in a fixed time interval of a zero-mean Gaussian stationary process. In this study we use the so-called independent interval approximation to go beyond Rice's result and derive analytic expressions for all higher-order zero-crossing cumulants and moments. Our results agree well with simulations for the non-Markovian autoregressive model.

Place, publisher, year, edition, pages
American Physical Society, 2018. Vol. 97, no 3, article id 032114
National Category
Probability Theory and Statistics
Identifiers
URN: urn:nbn:se:umu:diva-146439DOI: 10.1103/PhysRevE.97.032114ISI: 000427356800004OAI: oai:DiVA.org:umu-146439DiVA, id: diva2:1203888
Available from: 2018-05-04 Created: 2018-05-04 Last updated: 2018-06-09Bibliographically approved

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Nyberg, MarkusLizana, Ludvig

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