Quantitative relative entropy estimates for interacting particle systems with common noise

We derive quantitative estimates proving the conditional propagation of chaos for large stochastic systems of interacting particles subject to both idiosyncratic and common noise. We obtain explicit bounds on the relative entropy between the conditional Liouville equation and the stochastic Fokker--...

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Bibliographic Details
Main Author Nikolaev, Paul
Format Journal Article
LanguageEnglish
Published 01.07.2024
Subjects
Mathematics - Analysis of PDEs
Mathematics - Probability
Online AccessGet full text
DOI10.48550/arxiv.2407.01217

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Summary:We derive quantitative estimates proving the conditional propagation of chaos for large stochastic systems of interacting particles subject to both idiosyncratic and common noise. We obtain explicit bounds on the relative entropy between the conditional Liouville equation and the stochastic Fokker--Planck equation with an interaction kernel \(kın L^2(^d) L^ınfty(^d)\), extending far beyond the Lipschitz case. Our method relies on reducing the problem to the idiosyncratic setting, which allows us to utilize the exponential law of large numbers by Jabin and Wang~JabinWang2018 in a pathwise manner.
DOI:10.48550/arxiv.2407.01217