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

Journal Article (2020)
Author(s)

F. Collet (Università degli Studi di Padova, TU Delft - Applied Probability)

RICHARD C. KRAAIJ (TU Delft - Applied Probability)

Research Group
Applied Probability
Copyright
© 2020 F. Collet, R.C. Kraaij
DOI related publication
https://doi.org/10.1016/j.spa.2019.11.008
More Info
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Publication Year
2020
Language
English
Copyright
© 2020 F. Collet, R.C. Kraaij
Research Group
Applied Probability
Bibliographical Note
Accepted author manuscript@en
Issue number
7
Volume number
130
Pages (from-to)
4028-4061
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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.

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