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Fractional Brownian Fields over Manifolds (1207.6419v3)
Published 26 Jul 2012 in math.PR
Abstract: Extensions of the fractional Brownian fields are constructed over a complete Riemannian manifold. This construction is carried out for the full range of the Hurst parameter $\alpha\in(0,1)$. In particular, we establish existence, distributional scaling (self-similiarity), stationarity of the increments, and almost sure H\"{o}lder continuity of sample paths. Stationary counterparts to these fields are also constructed.
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