English

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 α(0,1)\alpha\in(0,1). 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}
}
R2 v1 2026-06-21T21:42:18.656Z