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

L. Zunino, D. G. Pérez, M. T. Martín, A. Plastino, M. Garavaglia, and O. A. Rosso

Phys. Rev. E 75, 021115 – Published 20 February 2007

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.

Received 16 August 2006

DOI:https://doi.org/10.1103/PhysRevE.75.021115

Authors & Affiliations

L. Zunino^*

Centro de Investigaciones Ópticas, casilla de correo 124 Correo Central, 1900 La Plata, Argentina and Departamento de Ciencias Básicas, Facultad de Ingeniería, Universidad Nacional de La Plata (UNLP), 1900 La Plata, Argentina

D. G. Pérez^†

Instiuto de Física, Pontificia Universidad Católica de Valparaíso (PUCV), 23-40025 Valparaíso, Chile

M. T. Martín^‡ and A. Plastino^§

Instituto de Física, Facultad de Ciencias Exactas, Universidad Nacional de La Plata (UNLP), casilla de correo 727, 1900 La Plata, Argentina and Argentina’s National Research Council (CONICET), Argentina

M. Garavaglia^∥

Centro de Investigaciones Ópticas, casilla de correo 124 Correo Central, 1900 La Plata, Argentina and Departamento de Física, Facultad de Ciencias Exactas, Universidad Nacional de La Plata (UNLP), 1900 La Plata, Argentina

O. A. Rosso^¶

Chaos and Biology Group, Instituto de Cálculo, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires (UBA), Pabellón II, Ciudad Universitaria, 1428 Ciudad de Buenos Aires, Argentina

^*Also at Departamento de Física, Facultad de Ciencias Exactas, Universidad Nacional de La Plata (UNLP). Electronic address: lucianoz@ciop.unlp.edu.ar
^†Electronic address: dario.perez@ucv.cl
^‡Electronic address: mtmartin@fisica.unlp.edu.ar
^§Electronic address: plastino@fisica.unlp.edu.ar
^∥Electronic address: garavagliam@ciop.unlp.edu.ar
^¶Electronic address: oarosso@fibertel.com.ar

Article Text (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand

Issue

Vol. 75, Iss. 2 — February 2007

Reuse & Permissions

Access Options

Author publication services for translation and copyediting assistance advertisement

Physical Review E

covering statistical, nonlinear, biological, and soft matter physics