Quantitative relative entropy estimates for interacting particle systems with common noise

2024/07/01 by Paul Nikolaev, Nikolaev, Paul · 2 citations
Physics and Astronomy · Computer Science · #Statistical Mechanics and Entropy #Advanced Thermodynamics and Statistical Mechanics #Gaussian Processes and Bayesian Inference

paper · pdf · doi:10.48550/arxiv.2407.01217

Abstract

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 \(k∈ L²(\R^d) ∩ L^∞(\R^d)\), 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~\citeJabinWang2018 in a pathwise manner.

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