Series Expansions of Fractional Brownian Motions and Strong Local Nondeterminism of Bifractional Brownian Motions on Balls and Spheres

Abstract

This paper provides series expansions for fractional Brownian motions on the unit ball and the unit sphere by means of ultraspherical polynomials and spherical harmonics. It establishes the property of strong local nondeterminism of isotropic Gaussian random fields on the unit sphere and that of fractional and bifractional Brownian motions on the unit ball and the unit sphere.