Strong local nondeterminism of spherical fractional Brownian motion. (English) Zbl 1392.60034

Summary: Let \(B = \{B(x), x \in \mathbb{S}^2\}\) be the fractional Brownian motion indexed by the unit sphere \(\mathbb{S}^2\) with index \(0 < H \leq \frac{1}{2}\), introduced by J. Istas [Electron. Commun. Probab. 10, 254–262 (2005; Zbl 1112.60029)]. We establish optimal upper and lower bounds 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 \(B\).


60G22 Fractional processes, including fractional Brownian motion
60G60 Random fields
60G17 Sample path properties


Zbl 1112.60029
Full Text: DOI arXiv


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