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Effect of nonlinearity of discrete Langevin model on behavior of extremes in generated time series

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  • Czechowski, Zbigniew
  • Telesca, Luciano

Abstract

In this work we analyze the influence of nonlinearity on the behavior of extremal values of time series generated by two discrete Langevin models: fixing the diffusion function in the first (M1), the probability distribution function in the second (M2). The extremes were generated by applying the run theory. A mathematical relationship was found between nonlinearity of models and means and distributions of run lengths and inter-extreme times as well as with the clustering of extremes. Furthermore, the Allan factor curves of the extremes suggest that the sequences of extremes are fractal for timescales up to the mean inter-extreme time. Our main findings are that the variation of the nonlinearity parameter in model M1 (leading to the increase of the distribution tail length) can cause a significant variation of the extreme characteristics and an increase of the clustering while the variation of the nonlinearity parameter in model M2 (with fixed distribution) has a little effect on extremes.

Suggested Citation

  • Czechowski, Zbigniew & Telesca, Luciano, 2024. "Effect of nonlinearity of discrete Langevin model on behavior of extremes in generated time series," Chaos, Solitons & Fractals, Elsevier, vol. 183(C).
    • Handle: RePEc:eee:chsofr:v:183:y:2024:i:c:s096007792400479x
    DOI: 10.1016/j.chaos.2024.114927
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    References listed on IDEAS

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    1. Telesca, Luciano & Czechowski, Zbigniew, 2012. "Discriminating geoelectrical signals measured in seismic and aseismic areas by using Ito models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(3), pages 809-818.
    2. Xu, Pengfei & Gong, Xulu & Wang, Haotian & Li, Yiwei & Liu, Di, 2023. "A study of stochastic resonance in tri-stable generalized Langevin system," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 626(C).
    3. Bunde, Armin & F. Eichner, Jan & Havlin, Shlomo & Kantelhardt, Jan W., 2003. "The effect of long-term correlations on the return periods of rare events," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 330(1), pages 1-7.
    4. Czechowski, Zbigniew & Rozmarynowska, Aneta, 2008. "The importance of the privilege for appearance of inverse-power solutions in Ito equations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(22), pages 5403-5416.
    5. M. S. Santhanam & Holger Kantz, 2008. "Return interval distribution of extreme events and long term memory," Papers 0803.1706, arXiv.org.
    6. Czechowski, Zbigniew & Telesca, Luciano, 2011. "The construction of an Ito model for geoelectrical signals," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(13), pages 2511-2519.
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