Approximations of fractional Brownian motion

Details Approximations of fractional Brownian motion Approximations of fractional Brownian motion

2012-01-04

arxiv.org/abs/1201.0872v1

Bernoulli 2011, Vol. 17, No. 4, 1195-1216

Mathematics

Statistics Theory

Published in at http://dx.doi.org/10.3150/10-BEJ319 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statisti

Scientific paper

10.3150/10-BEJ319

Approximations of fractional Brownian motion using Poisson processes whose parameter sets have the same dimensions as the approximated processes have been studied in the literature. In this paper, a special approximation to the one-parameter fractional Brownian motion is constructed using a two-parameter Poisson process. The proof involves the tightness and identification of finite-dimensional distributions.

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