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Uniqueness of Fokker-Planck equations for spin lattice systems (II): Non-compact case

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Abstract

We study the existence and uniqueness of solutions for a class of infinite-dimensional Fokker-Planck equations on the spin lattice systems \(M^{\mathbb{Z}^d }\), where the spin space M is a non-compact Riemannian manifold. The method is based on the Stroock-Varadhan’s martingale approach, some compactness results of the general theory developed by Ethier-Kurtz, and some a priori gradient estimates.

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Authors and Affiliations

  1. Engineering Faculty of Hunedoara, Politehnica University of Timişoara, Hunedoara, 331128, Romania

    Ludovic Dan Lemle

  2. School of Mathematical Sciences, University of Science and Technology of China, Hefei, 230026, China

    Ran Wang

  3. Institute of Applied Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, China

    LiMing Wu

  4. Laboratoire de Math. CNRS-UMR 6620, Université Blaise Pascal, Aubière, 63177, France

    LiMing Wu

Authors
  1. Ludovic Dan Lemle
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  2. Ran Wang
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  3. LiMing Wu
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Correspondence to Ran Wang.

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Lemle, L.D., Wang, R. & Wu, L. Uniqueness of Fokker-Planck equations for spin lattice systems (II): Non-compact case. Sci. China Math. 57, 161–172 (2014). https://doi.org/10.1007/s11425-013-4745-3

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