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

L. ZUNINO; D. G. PEREZ; M, T. MARTIN; A. PLASTINO; M. GARAVAGLIA; O. A. ROSSO

PHYSICAL REVIEW E - STATISTICAL PHYSICS, PLASMAS, FLUIDS AND RELATED INTERDISCIPLINARY TOPICS

The American Physical Society

Año: 2007 vol. 75 p. 1 - 10

1063-651X

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.