LARGE DEVIATIONS FOR INTERACTING DIFFUSIONS WITH PATH-DEPENDENT MCKEAN-VLASOV LIMIT

• 成果类型: Article
• 署名作者: Baldasso, Rangel; Pereira, Alan; Reis, Guilherme
• 署名单位: Bar Ilan University; Universidade Federal de Alagoas; Universidade Federal da Bahia
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/21-AAP1692
• 发表日期: 2022
• 页码: 665-695
• 关键词: Random graphs; propagation; networks; chaos

摘要

We consider a mean-field system of path-dependent stochastic interacting diffusions in random media over a finite time window. The interaction term is given as a function of the empirical measure and is allowed to be nonlinear and path dependent. We prove that the sequence of empirical measures of the full trajectories satisfies a large deviation principle with explicit rate function. The minimizer of the rate function is characterized as the path-dependent McKean-Vlasov diffusion associated to the system. As corollary, we obtain a strong law of large numbers for the sequence of empirical measures. The proof is based on a decoupling technique by associating to the system a convenient family of product measures. To illustrate, we apply our results for the delayed stochastic Kuramoto model and for a SDE version of Galves-Locherbach model.