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Revista Colombiana de Estadística

Print version ISSN 0120-1751

Rev.Colomb.Estad. vol.28 no.2 Bogotá July/Dec. 2005

 

Hoja browniana fraccional

Fractional Brownian Sheet

LILIANA BLANCO CASTAÑEDA1, JOHANNA GARZÓN MERCHÁN2

1Departamento de Estadística, Universidad Nacional de Colombia, Bogotá. E-mail: lblancoc@unal.edu.co.
2 Departamento de Matemáticas, Universidad Nacional de Colombia, Bogotá. E-mail: mjgarzonm@unal.edu.co.


Resumen

Se presenta la hoja browniana fraccional (hBf) o movimiento browniano fraccional en dos parámetros y algunas de sus propiedades importantes como son la autosimilaridad y la estacionaridad de los incrementos. Se incluyen además dos representaciones de la hBf, análogas a la representación en pro medio móvil y en intervalo finito del movimiento browniano fraccional.

Palabras Clave: Movimiento browniano fraccional, procesos estocásticos en dos parámetros, hoja browniana, procesos autosimilares, procesos con incrementos estacionarios.


Abstract

Fractional brownian sheet or two parameter fractional brownian motion and some important properties with selfsimilar and stationary increments are presented. Moreover, two representations for hBf analogous to moving average and on an interval representations for fractional brownian motion are included.

Keywords: Fractional Brownian motion, two-parameter stochastic proces ses, Brownian sheet, selfsimilary processes, stationary increments processes.


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