Convergence to equilibrium for granular media equations and their Euler schemes

• 成果类型: Article
• 署名作者: Malrieu, F
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/aoap/1050689593
• 发表日期: 2003
• 页码: 540-560
• 关键词: self-stabilizing processes; invariant probability

摘要

We introduce a new interacting particle system to investigate the behavior of the nonlinear, nonlocal diffusive equation already studied by Benachour et al. [3, 4]. We first prove an uniform (with respect to time) propagation of chaos. Then, we show that the solution of the nonlinear PDE converges exponentially fast to equilibrium recovering a result established by an other way by Carrillo, McCann and Vilanni [7]. At last we provide explicit and Gaussian confidence intervals for the convergence of an implicit Euler scheme to the stationary distribution of the nonlinear equation.