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Spectral analysis and generation of certain highly oscillatory curves related to chaos

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  • Chen, Goong
  • Mariani, Maria Christina
  • SenGupta, Indranil
  • Mai, Nicholas

Abstract

Highly oscillatory phenomena are omnipresent in applications. Two important underlying sources are stochastic fluctuations and deterministic randomness. In this paper, we will present heuristics, theorems, and a few illustrations on the Fourier spectrum and deterministic random time series, based upon our understanding of certain rapid oscillations in chaos.

Suggested Citation

  • Chen, Goong & Mariani, Maria Christina & SenGupta, Indranil & Mai, Nicholas, 2012. "Spectral analysis and generation of certain highly oscillatory curves related to chaos," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(4), pages 1453-1468.
    • Handle: RePEc:eee:phsmap:v:391:y:2012:i:4:p:1453-1468
    DOI: 10.1016/j.physa.2011.11.013
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    References listed on IDEAS

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    1. Mariani, M.C. & Florescu, I. & Beccar Varela, M.P. & Ncheuguim, E., 2009. "Long correlations and Levy models applied to the study of memory effects in high frequency (tick) data," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(8), pages 1659-1664.
    2. Ionuţ Florescu & Maria Cristina Mariani & Granville Sewell, 2011. "Numerical solutions to an integro-differential parabolic problem arising in the pricing of financial options in a Levy market," Quantitative Finance, Taylor & Francis Journals, vol. 14(8), pages 1445-1452, August.
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