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

Francesca Collet, Richard C. Kraaij

Research output: Contribution to journalArticleScientificpeer-review

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.

Original languageEnglish
Pages (from-to)4028-4061
Number of pages34
JournalStochastic Processes and their Applications
Volume130
Issue number7
DOIs
Publication statusPublished - 2020

Keywords

  • Bifurcation of periodic orbits
  • Hamilton–Jacobi equation
  • Interacting particle systems
  • Mean-field interaction
  • Moderate deviations
  • Perturbation theory for Markov processes

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