A wavelet-based approximation of fractional Brownian motion with a parallel algorithm
| Autor: | Hong, Dawei, Man, Shushuang, Birget, Jean-Camille, Lun, Desmond |
|---|---|
| Rok vydání: | 2011 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | We construct a wavelet-based almost sure uniform approximation of fractional Brownian motion (fBm) B_t^(H), t in [0, 1], of Hurst index H in (0, 1). Our results show that by Haar wavelets which merely have one vanishing moment, an almost sure uniform expansion of fBm of H in (0, 1) can be established. The convergence rate of our approximation is derived. We also describe a parallel algorithm that generates sample paths of an fBm efficiently. Comment: 20 pages. J. of Applied Probability, to appear in March 2014 |
| Databáze: | arXiv |
| Externí odkaz: |
|