Let $B = \left\{ B\left( x\right),\, x\in \mathbb{ S}^{ 2}\right\} $ be the fractional Brownian motion indexed by the unit sphere $\mathbb{ S}^{ 2}$ with index $0<H\leq \frac{ 1}{ 2}$, 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 $B$.
Categories: math.ST stat.TH