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Face of Tobias Ambjörnsson. Photo.

Tobias Ambjörnsson

Senior lecturer

Face of Tobias Ambjörnsson. Photo.

Zero-crossing statistics for non-Markovian time series

Author

  • Markus Nyberg
  • Ludvig Lizana
  • Tobias Ambjörnsson

Summary, in English

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.

Department/s

  • Department of Astronomy and Theoretical Physics

Publishing year

2018-03-14

Language

English

Publication/Series

Physical Review E

Volume

97

Issue

3

Document type

Journal article

Publisher

American Physical Society

Topic

  • Computational Mathematics

Status

Published

ISBN/ISSN/Other

  • ISSN: 2470-0045