Approximations of fractional Brownian motion

Yuqiang Li; Hongshuai Dai

doi:10.3150/10-bej319

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arXiv · 1201.0872

Approximations of fractional Brownian motion

Yuqiang Li·Hongshuai Dai

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Abstract

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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Yuqiang Li, Hongshuai Dai. 2012-01-04. Approximations of fractional Brownian motion. https://doi.org/10.3150/10-bej319

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