¹Estudiante. Maestría en Matemáticas. Universidad Nacional de Colombia, Sede Bogotá. E- mail: andrea.cavanzo@gmail.com
² Profesora. Departamento de Estadística. Universidad Nacional de Colombia, Sede Bogotá. E-mail: lblancoc@unal.edu.co

Se hace un estudio detallado de algunas construcciones significativas del movimiento browniano fraccional (mBf) desarrolladas recientemente: la de Taqqu (1975), quien construye el mBf como un límite de sumas parciales nor malizadas de variables aleatorias estacionarias, la de Sottinen (2003), quien utiliza una interpolación de variables aleatorias y la realizada por Delgado & Jolis (2000) quienes aproximan las distribuciones finito dimensionales del mBf a partir de las de procesos continuos definidos por medio de un proceso de Poisson.

Palabras Clave: Convergencia débil, proceso gausiano, proceso de Poisson, movimiento browniano fraccional, caminata aleatoria.

Some of the most significant constructions of the fractional brownian mo tion developed recently are reviewed in detail. Taqqu works with the limit under weak convergence of normalized partial sums of stationary random variables exhibiting long run non-periodic dependence. Sottinen proves a Donsker type approximation theorem and Delgado & Jolis prove that the fractional brownian motion can be weakly approximated by the law of some processes constructed from standard Poisson process.

Keywords: Weak Convergence, Gaussian Process, Poisson Process, Frac- tional Brownian Motion, Random Walk.

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