Fractional Brownian fields over manifolds

Gelbaum, Zachary

doi:10.1090/S0002-9947-2014-06106-0

Fractional Brownian fields over manifolds
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by Zachary A. Gelbaum PDF

Trans. Amer. Math. Soc. 366 (2014), 4781-4814 Request permission

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 Hölder continuity of sample paths. Stationary counterparts to these fields are also constructed.

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