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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 \(B\).

MSC:

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

Citations:

Zbl 1112.60029
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Full Text: DOI arXiv

References:

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