LARGE DEVIATION PROPERTIES OF WEAKLY INTERACTING PROCESSES VIA WEAK CONVERGENCE METHODS

• 成果类型: Article
• 署名作者: Budhiraja, Amarjit; Dupuis, Paul; Fischer, Markus
• 署名单位: University of North Carolina; University of North Carolina Chapel Hill; Brown University
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/10-AOP616
• 发表日期: 2012
• 页码: 74-102
• 关键词: navier-stokes equations; particle-systems; brownian-motion; DIFFUSIONS; LAW

摘要

We study large deviation properties of systems of weakly interacting particles modeled by Ito stochastic differential equations (SDEs). It is known under certain conditions that the corresponding sequence of empirical measures converges, as the number of particles tends to infinity, to the weak solution of an associated McKean-Vlasov equation. We derive a large deviation principle via the weak convergence approach. The proof, which avoids discretization arguments, is based on a representation theorem, weak convergence and ideas from stochastic optimal control. The method works under rather mild assumptions and also for models described by SDEs not of diffusion type. To illustrate this, we treat the case of SDEs with delay.