Published
2005-07-01
EL MOVIMIENTO BROWNIANO FRACCIONAL COMO LÍMITE DE CIERTOS TIPOS DE PROCESOS ESTOCÁSTICOS
THE BROWNIAN FRACTIONAL MOTION AS A LIMIT OF SOME TYPES OF
Keywords:
Convergencia débil, proceso gausiano, proceso de Poisson, movimiento browniano fraccional, caminata aleatoria (es)Weak Convergence, Gaussian Process, Poisson Process, Fractional Brownian Motion, Random Walk (en)
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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 normalizadas 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.
Some of the most significant constructions of the fractional brownian motion 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.
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How to Cite
Cavanzo Nisso, A., & Blanco Castañeda, L. (2005). THE BROWNIAN FRACTIONAL MOTION AS A LIMIT OF SOME TYPES OF. Revista Colombiana De Estadística, 28(2), 173-191. https://revistas.unal.edu.co/index.php/estad/article/view/28877
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