Strong Local Nondeterminism of Spherical Fractional Brownian Motion

Abstract

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 $0<H\le \frac{1}{2}$, introduced by Istas \cite{IstasECP05}. We establish optimal estimates for its angular power spectrum $\{d_{\ell },\ell =0,1,2,\dots \}$, and then exploit its high-frequency behavior to establish the property of its strong local nondeterminism of $B$.

References in corpus (1)

• On the overlap in the multiple spherical SK models