Uniqueness for a weak nonlinear evolution equation and large deviations for diffusing particles with electrostatic repulsion

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• 作者：Fontbona ; J.
• 关键词：60K35 ; 60F10 ; Singular McKean&ndash ; Vlasov model ; Nonlinear PDE ; Large deviations
• 刊名：Stochastic Processes and their Applications
• 出版年：2004
• 出版时间：July, 2004
• 年：2004
• 卷：112
• 期：1
• 页码：119-144
• 全文大小：379 K

文摘

We use hydrodynamics techniques to study the large deviations properties of the McKean–Vlasov model with singular interactions introduced by Cépa and Lépingle (Probab. Theory Related Fields 107 (1997) 429). In a general framework, we prove upper bounds and exponential tightness, and study the action functional. The study of lower bounds is much harder and requires a uniqueness result for a class of nonlinear evolution equations. In the case of interacting Ornstein–Uhlenbeck particles, we prove a general uniqueness statement by extending techniques of Cabannal-Duvillard and Guionnet (Ann. Probab. 29 (2001) 1205). Using this result we deduce some lower bounds for interacting particles with constant diffusion coefficient and general drift terms.