Isotropic Lévy processes on Riemannian manifolds

Applebaum, D.; Estrade, A.

Ann. Probab., Tome 28 (2000) no. 1, p. 166-184 / Harvested from Project Euclid

Résumé

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.

Publié le : 2000-01-14
Classification: Riemannian manifolds, orthonormal frame bundle, basic vector fields, geodesics, horizontal Lévy process, isotropic Lévy process, Feller semigroup, interlacing construction, 58G32, 60J25, 60E07, 58G35, 60G55

@article{1019160116,
     author = {Applebaum, D. and Estrade, A.},
     title = {Isotropic L\'evy processes on Riemannian manifolds},
     journal = {Ann. Probab.},
     volume = {28},
     number = {1},
     year = {2000},
     pages = { 166-184},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1019160116}
}

Applebaum, D.; Estrade, A. Isotropic Lévy processes on Riemannian manifolds. Ann. Probab., Tome 28 (2000) no. 1, pp.  166-184. http://gdmltest.u-ga.fr/item/1019160116/