A new approach to quantitative propagation of chaos for drift, diffusion and jump processes

• 成果类型: Article
• 署名作者: Mischler, Stephane; Mouhot, Clement; Wennberg, Bernt
• 署名单位: Universite PSL; Universite Paris-Dauphine; University of Cambridge; Chalmers University of Technology; University of Gothenburg
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-013-0542-8
• 发表日期: 2015
• 页码: 1-59
• 关键词: stochastic particle approximations; boltzmann-equation; probability metrics; granular media; CONVERGENCE; equilibrium; uniqueness; trend

摘要

This paper is devoted the study of the mean field limit for many-particle systems undergoing jump, drift or diffusion processes, as well as combinations of them. The main results are quantitative estimates on the decay of fluctuations around the deterministic limit and of correlations between particles, as the number of particles goes to infinity. To this end we introduce a general functional framework which reduces this question to the one of proving a purely functional estimate on some abstract generator operators (consistency estimate) together with fine stability estimates on the flow of the limiting nonlinear equation (stability estimates). Then we apply this method to a Boltzmann collision jump process (for Maxwell molecules), to a McKean-Vlasov drift-diffusion process and to an inelastic Boltzmann collision jump process with (stochastic) thermal bath. To our knowledge, our approach yields the first such quantitative results for a combination of jump and diffusion processes.