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

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:130

Article

Collet, Francesca^1,2  Kraaij, Richard C.¹ 

[1] Delft Univ Technol, Delft Inst Appl Math, van Mourik Broekmanweg 6, NL-2628 XE Delft, Netherlands

[2] Univ Padua, Dept Math Tullio Levi Civita, Via Trieste 63, I-35121 Padua, Italy

关键词: Moderate deviations;    Interacting particle systems;    Mean-field interaction;    Bifurcation of periodic orbits;    Hamilton-Jacobi equation;    Perturbation theory for Markov processes;   

DOI  :  10.1016/j.spa.2019.11.008

来源: Elsevier

【 摘 要 】

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. (C) 2019 Elsevier B.V. All rights reserved.

【 授权许可】

Free