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Classical large deviation theorems on complete Riemannian manifolds

Author

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  • Kraaij, Richard C.
  • Redig, Frank
  • Versendaal, Rik

Abstract

We generalize classical large deviation theorems to the setting of complete, smooth Riemannian manifolds. We prove the analogue of Mogulskii’s theorem for geodesic random walks via a general approach using viscosity solutions for Hamilton–Jacobi equations. As a corollary, we also obtain the analogue of Cramér’s theorem. The approach also provides a new proof of Schilder’s theorem. Additionally, we provide a proof of Schilder’s theorem by using an embedding into Euclidean space, together with Freidlin–Wentzell theory.

Suggested Citation

  • Kraaij, Richard C. & Redig, Frank & Versendaal, Rik, 2019. "Classical large deviation theorems on complete Riemannian manifolds," Stochastic Processes and their Applications, Elsevier, vol. 129(11), pages 4294-4334.
    • Handle: RePEc:eee:spapps:v:129:y:2019:i:11:p:4294-4334
    DOI: 10.1016/j.spa.2018.11.019
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    References listed on IDEAS

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    1. Collet, Francesca & Kraaij, Richard C., 2017. "Dynamical moderate deviations for the Curie–Weiss model," Stochastic Processes and their Applications, Elsevier, vol. 127(9), pages 2900-2925.
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    Cited by:

    1. Collet, Francesca & Kraaij, Richard C., 2020. "Path-space moderate deviations for a class of Curie–Weiss models with dissipation," Stochastic Processes and their Applications, Elsevier, vol. 130(7), pages 4028-4061.
    2. Kraaij, Richard C. & Mahé, Louis, 2020. "Well-posedness of Hamilton–Jacobi equations in population dynamics and applications to large deviations," Stochastic Processes and their Applications, Elsevier, vol. 130(9), pages 5453-5491.

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