Regularity of Gaussian Processes on Dirichlet spaces
Probability
2015-08-05 v1
Abstract
We are interested in the regularity of centered Gaussian processes (Z_x), x in M indexed by compact metric spaces M. It is shown that the almost everywhere Besov space regularity of such a process is (almost) equivalent to the Besov regularity of the covariance K(x,y) = E(Z_xZ_y) under the assumption that (i) there is an underlying Dirichlet structure on M which determines the Besov space regularity, and (ii) the operator K with kernel K(x,y) and the underlying operator A of the Dirichlet structure commute. As an application of this result we establish the Besov regularity of Gaussian processes indexed by compact homogeneous spaces and, in particular, by the sphere.
Keywords
Cite
@article{arxiv.1508.00822,
title = {Regularity of Gaussian Processes on Dirichlet spaces},
author = {Gerard Kerkyacharian and Shigeyoshi Ogawa and Pencho Petrushev and Dominique Picard},
journal= {arXiv preprint arXiv:1508.00822},
year = {2015}
}