Strong Local Nondeterminism of Spherical Fractional Brownian Motion

Let $B=\{B\left(x\right),x\in {\mathbb{S}}^2\}$ be the fractional Brownian motion indexed by the unit sphere ${\mathbb{S}}^2$ with index $0<H\le \frac{1}{2}$, introduced by Istas \cite{IstasECP05}. We establish optimal estimates for its angular power spectrum ${d_\ell, \ell = 0, 1, 2, \ldots}$, and then exploit its high-frequency behavior to establish the property of its strong local nondeterminism of $B$.