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Path-space moderate deviations for a class of Curie–Weiss models with dissipation

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  • Collet, Francesca
  • Kraaij, Richard C.

Abstract

We modify the spin-flip dynamics of the Curie–Weiss model with dissipation in Dai Pra, Fischer and Regoli (2013) by considering arbitrary transition rates and we analyze the phase-portrait as well as the dynamics of moderate fluctuations for macroscopic observables. We obtain path-space moderate deviation principles via a general analytic approach based on the convergence of non-linear generators and uniqueness of viscosity solutions for associated Hamilton–Jacobi equations. The moderate asymptotics depend crucially on the phase we are considering and, moreover, their behavior may be influenced by the choice of the rates.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:spapps:v:130:y:2020:i:7:p:4028-4061
    DOI: 10.1016/j.spa.2019.11.008
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    References listed on IDEAS

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    1. Ditlevsen, Susanne & Löcherbach, Eva, 2017. "Multi-class oscillating systems of interacting neurons," Stochastic Processes and their Applications, Elsevier, vol. 127(6), pages 1840-1869.
    2. Dai Pra, Paolo & Tovazzi, Daniele, 2019. "The dynamics of critical fluctuations in asymmetric Curie–Weiss models," Stochastic Processes and their Applications, Elsevier, vol. 129(3), pages 1060-1095.
    3. Paolo Dai Pra & Elena Sartori & Marco Tolotti, 2019. "Climb on the Bandwagon: Consensus and Periodicity in a Lifetime Utility Model with Strategic Interactions," Dynamic Games and Applications, Springer, vol. 9(4), pages 1061-1075, December.
    4. 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.
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