A wavelet-based approximation of fractional Brownian motion with a parallel algorithm

Details A wavelet-based approximation of fractional Brownian motion with a parallel algorithm A wavelet-based approximation of fractional Brownian motion with a parallel algorithm

2011-11-28

arxiv.org/abs/1111.6331v2

Mathematics

Probability

20 pages

Scientific paper

We construct a wavelet-based expansion to approximate fractional Brownian
motion of Hurst index H in (0, 1). For practical implementations, the expansion
converges almost surely and uniformly in discrete time t in [0, 1]. We prove
that the convergence rate is optimal. We also show that the approximation can
be implemented by a fast parallel algorithm.

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