Fractional Brownian Fields over Manifolds
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 α∈(0,1). In particular, we establish existence, distributional scaling (self-similiarity), stationarity of the increments, and almost sure H\"older continuity of sample paths. Stationary counterparts to these fields are also constructed.
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