Simulation paradoxes related to a fractional Brownian motion with small Hurst index

Vitalii Makogin

doi:10.15559/16-VMSTA59

Simulation paradoxes related to a fractional Brownian motion with small Hurst index

Probability 2016-07-14 v1

Authors: Vitalii Makogin

View on arXiv ↗ PDF ↗ DOI ↗

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 $\infty$ as the Hurst index tends to 0.

Keywords

fractional Brownian motion Hurst index sample path simulation expected maximum approximation error

Cite

@article{arxiv.1607.03631,
  title  = {Simulation paradoxes related to a fractional Brownian motion with small Hurst index},
  author = {Vitalii Makogin},
  journal= {arXiv preprint arXiv:1607.03631},
  year   = {2016}
}

Comments

Published at http://dx.doi.org/10.15559/16-VMSTA59 in the Modern Stochastics: Theory and Applications (https://www.i-journals.org/vtxpp/VMSTA) by VTeX (http://www.vtex.lt/)

Related papers

View all related →