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

Author

Listed:
  • David Applebaum

    (University of Sheffield)

  • Rosemary Shewell Brockway

    (University of Sheffield)

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

Suggested Citation

  • David Applebaum & Rosemary Shewell Brockway, 2021. "$$L^2$$ L 2 Properties of Lévy Generators on Compact Riemannian Manifolds," Journal of Theoretical Probability, Springer, vol. 34(2), pages 1029-1042, June.
    • Handle: RePEc:spr:jotpro:v:34:y:2021:i:2:d:10.1007_s10959-019-00980-3
    DOI: 10.1007/s10959-019-00980-3
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    References listed on IDEAS

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    1. Mohari, Anilesh, 2003. "Ergodicity of homogeneous Brownian flows," Stochastic Processes and their Applications, Elsevier, vol. 105(1), pages 99-116, May.
    2. Mohari, Anilesh, 2004. "Ergodicity of Lévy flows," Stochastic Processes and their Applications, Elsevier, vol. 112(2), pages 245-259, August.
    3. David Applebaum, 2000. "Compound Poisson Processes and Lévy Processes in Groups and Symmetric Spaces," Journal of Theoretical Probability, Springer, vol. 13(2), pages 383-425, April.
    Full references (including those not matched with items on IDEAS)

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    1. Mohari, Anilesh, 2004. "Ergodicity of Lévy flows," Stochastic Processes and their Applications, Elsevier, vol. 112(2), pages 245-259, August.

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