Fractional Brownian Fields over Manifolds
Probability
2013-02-19 v3
Abstract
Extensions of the fractional Brownian fields are constructed over a complete Riemannian manifold. This construction is carried out for the full range of the Hurst parameter . In particular, we establish existence, distributional scaling (self-similiarity), stationarity of the increments, and almost sure H\"{o}lder continuity of sample paths. Stationary counterparts to these fields are also constructed.
Keywords
Cite
@article{arxiv.1207.6419,
title = {Fractional Brownian Fields over Manifolds},
author = {Zachary Gelbaum},
journal= {arXiv preprint arXiv:1207.6419},
year = {2013}
}