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

Francesca Collet; Richard C. Kraaij

doi:10.1016/j.spa.2019.11.008

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

Francesca Collet, Richard C. Kraaij^*

^*Corresponding author for this work

Applied Probability

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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.

Original language	English
Pages (from-to)	4028-4061
Number of pages	34
Journal	Stochastic Processes and their Applications
Volume	130
Issue number	7
DOIs	https://doi.org/10.1016/j.spa.2019.11.008
Publication status	Published - 2020

Bibliographical note

Accepted author manuscript

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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10.1016/j.spa.2019.11.008

Revision_Dissipative_CW_251119_finalAccepted author manuscript, 612 KBLicence: CC BY-NC-ND

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title = "Path-space moderate deviations for a class of Curie–Weiss models with dissipation",

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

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year = "2020",

doi = "10.1016/j.spa.2019.11.008",

language = "English",

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journal = "Stochastic Processes and their Applications",

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T1 - Path-space moderate deviations for a class of Curie–Weiss models with dissipation

AU - Collet, Francesca

AU - Kraaij, Richard C.

N1 - Accepted author manuscript

PY - 2020

Y1 - 2020

N2 - 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.

AB - 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.

KW - Bifurcation of periodic orbits

KW - Hamilton–Jacobi equation

KW - Interacting particle systems

KW - Mean-field interaction

KW - Moderate deviations

KW - Perturbation theory for Markov processes

UR - http://www.scopus.com/inward/record.url?scp=85076507355&partnerID=8YFLogxK

U2 - 10.1016/j.spa.2019.11.008

DO - 10.1016/j.spa.2019.11.008

M3 - Article

SN - 0304-4149

VL - 130

SP - 4028

EP - 4061

JO - Stochastic Processes and their Applications

JF - Stochastic Processes and their Applications

IS - 7

ER -

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

Abstract

Bibliographical note

Keywords

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