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Related Experiment Videos

Records in fractal stochastic processes.

A Aliakbari1, P Manshour1, M J Salehi1

  • 1Department of Physics, Faculty of Sciences, Persian Gulf University, 75169 Bushehr, Iran.

Chaos (Woodbury, N.Y.)
|April 3, 2017
PubMed
Summary

Record dynamics in fractal time series show universal behavior for stationary processes. For non-stationary processes, memory critically influences record statistics, especially with higher Hurst exponents.

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Area of Science:

  • Stochastic Processes
  • Time Series Analysis
  • Fractal Dynamics

Background:

  • Record statistics are crucial for understanding complex systems.
  • Fractal time series exhibit long-range dependence, impacting statistical properties.
  • Distinguishing between stationary and non-stationary fractal processes is key.

Purpose of the Study:

  • To investigate and compare record statistics in stationary and non-stationary fractal time series.
  • To identify the role of memory and Hurst exponents in record dynamics.
  • To understand the conditions under which memory influences record statistics.

Main Methods:

  • Analysis of record dynamics concepts.
  • Calculation of statistical properties for stationary fractional Gaussian noises.
  • Investigation of non-stationary fractional Brownian motions with varying memory and Hurst exponents.

Main Results:

  • Stationary fractional Gaussian noises exhibit universal record behavior across Hurst exponents.
  • Non-stationary fractional Brownian motions show record dynamics dependent on memory, acting as a non-stationarity index.
  • Deviation from stationary behavior increases with the Hurst exponent in non-stationary cases.

Conclusions:

  • Memory significantly governs record dynamics in fractal stochastic processes when it induces non-stationarity.
  • In stationary processes, memory's impact on record statistics is negligible.
  • The Hurst exponent modulates the influence of memory on record dynamics in non-stationary fractal time series.

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