The Brownian Fractional Motion as a Limit of some
Types of Stochastic Processes
Andrea Cavanzo & Liliana Blanco
Abstract
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.
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