Characterization of Gaussian self-similar stochastic processes using wavelet-based informational tools

L. Zunino, DARIO GABRIEL PEREZ , M. T. Martín, A. Plastino, M. Garavaglia, O. A. Rosso

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32 Scopus citations

Abstract

Efficient tools to characterize stochastic processes are discussed. Quantifiers originally proposed within the framework of information theory, like entropy and statistical complexity, are translated into wavelet language, which renders the above quantifiers into tools that exhibit the important "localization" advantages provided by wavelet theory. Two important and popular stochastic processes, fractional Brownian motion and fractional Gaussian noise, are studied using these wavelet-based informational tools. Exact analytical expressions are obtained for the wavelet probability distribution. Finally, numerical simulations are used to validate our analytical results.

Original languageEnglish
Article number021115
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Volume75
Issue number2
DOIs
StatePublished - 20 Feb 2007

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