The Annals of Probability

Isotropic Lévy processes on Riemannian manifolds

D. Applebaum and A. Estrade

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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.

Article information

Source
Ann. Probab., Volume 28, Number 1 (2000), 166-184.

Dates
First available in Project Euclid: 18 April 2002

Permanent link to this document
https://projecteuclid.org/euclid.aop/1019160116

Digital Object Identifier
doi:10.1214/aop/1019160116

Mathematical Reviews number (MathSciNet)
MR1756002

Zentralblatt MATH identifier
1044.60035

Subjects
Primary: 58G32 60J25: Continuous-time Markov processes on general state spaces 60E07: Infinitely divisible distributions; stable distributions
Secondary: 58G35 60G55: Point processes

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

Citation

Applebaum, D.; Estrade, A. Isotropic Lévy processes on Riemannian manifolds. Ann. Probab. 28 (2000), no. 1, 166--184. doi:10.1214/aop/1019160116. https://projecteuclid.org/euclid.aop/1019160116


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References

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