Quantitative estimates of propagation of chaos for stochastic systems with W-1,∞\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb}…
By Pierre-Emmanuel Jabin, Zhenfu Wang. Inventiones Mathematicae, 2017
254 citations recorded by the source corpus.
We derive quantitative estimates proving the propagation of chaos for large stochastic systems of interacting particles. We obtain explicit bounds on the relative entropy between the joint law of the particles and the tensorized law at the limit. We have to develop for this new laws of large numbers at the exponential scale. But our result only requires very weak regularity on the interaction kernel in the negative Sobolev space W˙-1,∞\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\dot{W}^{-1,\infty }$$\end{document}, thus including the Biot–Savart law and the point vortices dynamics for the 2d incompressible Navier–Stokes.
Subfields: Applied Mathematics, Control and Systems Engineering
View Paper: https://www.semanticscholar.org/paper/4011a1fdfec4228f328b3ffd2ea9b226818f2523
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Citations in the corpus
- Distribution dependent SDEs driven by additive fractional Brownian motion (2021, methodology): “On the one hand, new methods based on entropy inequalities [6, 14, 28] and modulated energy methods [41, 42] have allowed for the rigorous derivation of mean field limits for fairly singular B; while on the other, DDSDEs with irregular drifts are related to the flourishing field of regularization by”
- Large and Moderate Deviation Principles for McKean-Vlasov SDEs with Jumps (2020, background): “One can refer to [13, 26, 32, 50, 52] and the references therein for the existence and uniqueness of solutions to MVSDEs, [2, 21, 34, 48, 49, 57] for propagation of chaos, [22–25, 30, 40, 43–45, 55] for exponential ergodicity and functional inequalities, [1, 20, 28, 42, 56] and the references therei”