Sampling fractional Brownian motion in presence of absorption: a Markov Chain method
Abstract
We study fractional Brownian motion (fBm) characterized by the Hurst exponent H. Using a Monte Carlo sampling technique, we are able to numerically generate fBm processes with an absorbing boundary at the origin at discrete times for a large number of 10^7 time steps even for small values like H=1/4. The results are compatible with previous analytical results that the distribution of (rescaled) endpoints y follow a power law P(y) y^\phi with \phi=(1-H)/H, even for small values of H. Furthermore, for the case H=0.5 we also study analytically the finite-length corrections to the first order, namely a plateau of P(y) for y->0 which decreases with increasing process length. These corrections are compatible with the numerical results.
Keywords
Cite
@article{arxiv.1303.1648,
title = {Sampling fractional Brownian motion in presence of absorption: a Markov Chain method},
author = {Alexander K. Hartmann and Satya N. Majumdar and Alberto Rosso},
journal= {arXiv preprint arXiv:1303.1648},
year = {2015}
}
Comments
9 pages, 8 figures; (v3: two addition values of H simulated, extrapolation of phi for H<1/2)