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

Francesca Collet and Richard C. Kraaij

Stochastic Processes and their Applications, 2020, vol. 130, issue 7, 4028-4061

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.

Keywords: Moderate deviations; Interacting particle systems; Mean-field interaction; Bifurcation of periodic orbits; Hamilton–Jacobi equation; Perturbation theory for Markov processes (search for similar items in EconPapers)
Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:130:y:2020:i:7:p:4028-4061

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DOI: 10.1016/j.spa.2019.11.008

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