CONVERGENCE TO THE EQUILIBRIA FOR SELF-STABILIZING PROCESSES IN DOUBLE-WELL LANDSCAPE

• 成果类型: Article
• 署名作者: Tugaut, Julian
• 署名单位: University of Bielefeld
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/12-AOP749
• 发表日期: 2013
• 页码: 1427-1460
• 关键词: logarithmic sobolev inequalities; nonlinear parabolic equations; granular media equations; small-noise limit; invariant probability; diffusion-processes; stationary measures; propagation; models; chaos

摘要

We investigate the convergence of McKean-Vlasov diffusions in a non-convex landscape. These processes are linked to nonlinear partial differential equations. According to our previous results, there are at least three stationary measures under simple assumptions. Hence, the convergence problem is not classical like in the convex case. By using the method in Benedetto et al. [J. Statist. Phys. 91 (1998) 1261-1271] about the monotonicity of the free-energy, and combining this with a complete description of the set of the stationary measures, we prove the global convergence of the self-stabilizing processes.