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 Electronic Communications in Probability > Vol. 10 (2005) > Paper 26 open journal systems 


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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Pages: 254-262

Published on: December 21, 2005





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Electronic Communications in Probability. ISSN: 1083-589X