PROPAGATION OF CHAOS FOR MEAN FIELD ROUGH DIFFERENTIAL EQUATIONS

• 成果类型: Article
• 署名作者: Bailleul, Ismael; Catellier, Remi; Delarue, Francois
• 署名单位: Centre National de la Recherche Scientifique (CNRS); Universite de Rennes; Centre National de la Recherche Scientifique (CNRS); Universite Cote d'Azur
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/20-AOP1465
• 发表日期: 2021
• 页码: 944-996
• 关键词: geometry; driven; CONVERGENCE

摘要

We address propagation of chaos for large systems of rough differential equations associated with random rough differential equations of mean field type dX(t) = V(X-t, L(X-t)) dt + F(X-t, L(X-t)) dW(t), where W is a random rough path and L(X-t) is the law of X-t. We prove propagation of chaos, and provide also an explicit optimal convergence rate. The analysis is based upon the tools we developed in our companion paper (Electron. J. Probab. 25 (2020) 21) for solving mean field rough differential equations and in particular upon a corresponding version of the Ito-Lyons continuity theorem. The rate of convergence is obtained by a coupling argument developed first by Sznitman for particle systems with Brownian inputs.