Applebaum, D. and Brockway, R.S. (2021) L2 properties of Lévy generators on compact Riemannian manifolds. Journal of Theoretical Probability, 34 (2). pp. 1029-1042. ISSN 0894-9840
Abstract
We consider isotropic Lévy processes on a compact Riemannian manifold, obtained from an Rd-valued Lévy process through rolling without slipping. We prove that the Feller semigroups associated with these processes extend to strongly continuous contraction semigroups on Lp, for 1≤p<∞. When p=2, we show that these semigroups are self-adjoint. If, in addition, the motion has a non-trivial Brownian part, we prove that the generator has a discrete spectrum of eigenvalues and that the semigroup is trace-class.
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Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © The Author(s) 2020. This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/. |
Keywords: | Riemannian manifold; Frame bundle; Connection; Horizontal vector field; Lévy process; Lévy measure; Feller semigroup; Generator; Sobolev space; Transition density |
Dates: |
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Institution: | The University of Sheffield |
Academic Units: | The University of Sheffield > Faculty of Science (Sheffield) > School of Mathematics and Statistics (Sheffield) |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 05 Mar 2020 16:25 |
Last Modified: | 07 Dec 2021 17:09 |
Status: | Published |
Publisher: | Springer Science and Business Media LLC |
Refereed: | Yes |
Identification Number: | 10.1007/s10959-019-00980-3 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:156448 |
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