Spherical and Hyperbolic Fractional Brownian Motion
Jacques Istas, Université Pierre Mendès
Abstract
We define a Fractional Brownian Motion indexed by a sphere, or more
generally by a compact rank one symmetric space, and prove
that it exists if, and only if, 0< H leq 1/2. We then prove that
Fractional Brownian Motion indexed by an hyperbolic space exists if,
and only if,
0 < H leq 1/2. At last, we prove that Fractional Brownian Motion
indexed by a real tree exists when 0 < H leq 1/2.
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