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Quantifying Non-Stationarity with Information Theory.

Carlos Granero-Belinchón1,2, Stéphane G Roux1, Nicolas B Garnier1

  • 1Laboratoire de Physique, CNRS, Universitè Claude Bernard Lyon 1, ENS de Lyon, Universitè de Lyon, F-69342 Lyon, France.

Entropy (Basel, Switzerland)
|December 24, 2021
PubMed
Summary
This summary is machine-generated.

We developed a new information theory index to measure the stationarity of stochastic processes. This multi-scale index quantifies process regularity and non-stationarity, applicable to fluid turbulence.

Keywords:
entropyentropy ratemulti-scaleregularitystationarityturbulence

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Area of Science:

  • Physics
  • Information Theory
  • Data Analysis

Background:

  • Stochastic processes are fundamental in many scientific fields.
  • Quantifying stationarity is crucial for analyzing time series data.
  • Existing methods often rely on limited statistical moments.

Purpose of the Study:

  • To introduce a novel information theory-based index for quantifying process stationarity.
  • To develop a multi-scale measure that captures complete process dependencies.
  • To assess the index's utility in analyzing fluid turbulence.

Main Methods:

  • Utilizing information theory to compare information content in process increments.
  • Developing a multi-scale index by varying time scales (τ).
  • Applying the index to synthetic and experimental fluid turbulence data.

Main Results:

  • The index effectively quantifies process regularity at different scales.
  • It distinguishes between stationary and non-stationary processes.
  • The index's evolution across scales reveals the degree of roughness and non-stationarity.

Conclusions:

  • The proposed index offers a comprehensive measure of stochastic process stationarity.
  • It provides insights into process regularity and non-stationarity beyond traditional methods.
  • The index demonstrates practical applicability in fluid turbulence analysis.