Simulation paradoxes related to a fractional Brownian motion with small Hurst index
Volume 3, Issue 2 (2016), pp. 181–190
Pub. online: 4 July 2016
Type: Research Article
Open Access
Open Access
Received
31 May 2016
31 May 2016
Revised
19 June 2016
19 June 2016
Accepted
20 June 2016
20 June 2016
Published
4 July 2016
4 July 2016
Abstract
We consider the simulation of sample paths of a fractional Brownian motion with small values of the Hurst index and estimate the behavior of the expected maximum. We prove that, for each fixed N, the error of approximation $\mathbf{E}\max _{t\in [0,1]}{B}^{H}(t)-\mathbf{E}\max _{i=\overline{1,N}}{B}^{H}(i/N)$ grows rapidly to ∞ as the Hurst index tends to 0.
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