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January 2000 Isotropic Lévy processes on Riemannian manifolds
D. Applebaum, A. Estrade
Ann. Probab. 28(1): 166-184 (January 2000). DOI: 10.1214/aop/1019160116

Abstract

Under a natural invariance assumption on the Lévy measure we construct compound Poisson processes and more general isotropic Lévy processes on Riemannian manifolds by projection of a suitable horizontal process in the bundle of orthonormal frames.We characterize such Lévy processes through their infinitesimal generators and we show that they can be realized as the limit of a sequence of Brownian motions which are interlaced with jumps along geodesic segments.

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D. Applebaum. A. Estrade. "Isotropic Lévy processes on Riemannian manifolds." Ann. Probab. 28 (1) 166 - 184, January 2000. https://doi.org/10.1214/aop/1019160116

Information

Published: January 2000
First available in Project Euclid: 18 April 2002

zbMATH: 1044.60035
MathSciNet: MR1756002
Digital Object Identifier: 10.1214/aop/1019160116

Subjects:
Primary: 58G32 , 60E07 , 60J25
Secondary: 58G35 , 60G55

Keywords: basic vector fields , Feller semigroup , geodesics , horizontal Lévy process , interlacing construction , isotropic Lévy process , orthonormal frame bundle , Riemannian manifolds

Rights: Copyright © 2000 Institute of Mathematical Statistics

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Vol.28 • No. 1 • January 2000
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