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

J. Fontbona

Stochastic Processes and their Applications, 2004, vol. 112, issue 1, 119-144

Abstract: 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.

Keywords: Singular; McKean-Vlasov; model; Nonlinear; PDE; Large; deviations (search for similar items in EconPapers)
Date: 2004
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