The Brownian Fractional Motion as a Limit of some Types of Stochastic Processes
Andrea Cavanzo & Liliana Blanco
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.
Key words: Weak Convergence, Gaussian process, Poisson process, Fractional brownian motion, Random walk.