Quantitative relative entropy estimates for interacting particle systems with common noise

Byadmin
  • Authors: Paul Nikolaev
  • First public date: 2024-07-01
  • arXiv: 2407.01217
  • Preprint year: 2024
  • Status: Published
  • Publication type: Journal article
  • Publication year: 2025
  • Journal: SIAM Journal on Mathematical Analysis 57(3), 3071–3109 (2025)
  • DOI: 10.1137/24M1674650

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 \(k\in L^2(\R^d) \cap L^\infty(\R^d)\), 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~\cite{JabinWang2018} in a pathwise manner.

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BibTeX

@article{arxiv240701217,
  title = {Quantitative relative entropy estimates for interacting particle systems with common noise},
  author = {Paul Nikolaev},
  year = {2025},
  journal = {SIAM Journal on Mathematical Analysis 57(3), 3071–3109 (2025)},
  doi = {10.1137/24M1674650},
  eprint = {2407.01217},
  archivePrefix = {arXiv},
  primaryClass = {math.PR}
}

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