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arXiv · 1707.05021

Strong Local Nondeterminism of Spherical Fractional Brownian Motion

Xiaohong Lan·Yimin Xiao
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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 $0<H\leq \frac{1}{2}$, 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 $B$.

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Xiaohong Lan, Yimin Xiao. 2017-11-16. Strong Local Nondeterminism of Spherical Fractional Brownian Motion. https://arxiv.org/abs/1707.05021

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