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2005 Spherical and Hyperbolic Fractional Brownian Motion
Jacques Istas
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Electron. Commun. Probab. 10: 254-262 (2005). DOI: 10.1214/ECP.v10-1166

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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Jacques Istas. "Spherical and Hyperbolic Fractional Brownian Motion." Electron. Commun. Probab. 10 254 - 262, 2005. https://doi.org/10.1214/ECP.v10-1166

Information

Accepted: 21 December 2005; Published: 2005
First available in Project Euclid: 4 June 2016

zbMATH: 1112.60029
MathSciNet: MR2198600
Digital Object Identifier: 10.1214/ECP.v10-1166

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