$$L^2$$ L 2 Properties of Lévy Generators on Compact Riemannian Manifolds

David Applebaum () and Rosemary Shewell Brockway ()
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David Applebaum: University of Sheffield
Rosemary Shewell Brockway: University of Sheffield

Journal of Theoretical Probability, 2021, vol. 34, issue 2, 1029-1042

Abstract: Abstract We consider isotropic Lévy processes on a compact Riemannian manifold, obtained from an $${\mathbb {R}}^d$$ R d -valued Lévy process through rolling without slipping. We prove that the Feller semigroups associated with these processes extend to strongly continuous contraction semigroups on $$L^p$$ L p , for $$1\le p

Keywords: Riemannian manifold; Frame bundle; Connection; Horizontal vector field; Lévy process; Lévy measure; Feller semigroup; Generator; Sobolev space; Transition density; 58J65; 60G51; 47D07; 35P05; 60H10; 60J35 (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s10959-019-00980-3

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