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Characterization of Gaussian self-similar stochastic processes using wavelet-based informational tools
L Zunino1, D G Pérez, M T Martín
1Centro de Investigaciones Opticas, casilla de correo 124 Correo Central, 1900 La Plata, Argentina. lucianoz@ciop.unlp.edu.ar
This study introduces wavelet-based information theory tools to analyze complex stochastic processes. These methods offer enhanced localization for characterizing fractional Brownian motion and fractional Gaussian noise.
Area of Science:
- Information Theory
- Stochastic Processes
- Wavelet Analysis
Background:
- Characterizing complex stochastic processes is crucial in many scientific fields.
- Traditional information theory quantifiers lack spatial or temporal localization.
- Wavelet theory offers powerful localization properties.
Purpose of the Study:
- To develop and apply efficient wavelet-based tools for characterizing stochastic processes.
- To translate information theory quantifiers (entropy, statistical complexity) into wavelet language.
- To analyze fractional Brownian motion and fractional Gaussian noise using these novel tools.
Main Methods:
- Translation of information theory quantifiers into wavelet-based measures.
- Application of wavelet analysis to fractional Brownian motion and fractional Gaussian noise.
- Derivation of exact analytical expressions for wavelet probability distributions.
- Validation of analytical results through numerical simulations.
Main Results:
- Wavelet-based quantifiers provide enhanced "localization" advantages.
- Exact analytical expressions for wavelet probability distributions were obtained.
- The proposed methods successfully characterized fractional Brownian motion and fractional Gaussian noise.
Conclusions:
- Wavelet-based information theory offers efficient and localized tools for stochastic process characterization.
- The developed methods provide a robust framework for analyzing complex time series.
- Analytical and numerical results confirm the effectiveness of the wavelet approach.
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