SMOLUCHOWSKI-KRAMERS APPROXIMATION AND LARGE DEVIATIONS FOR INFINITE-DIMENSIONAL NONGRADIENT SYSTEMS WITH APPLICATIONS TO THE EXIT PROBLEM

• 成果类型: Article
• 署名作者: Cerrai, Sandra; Salins, Michael
• 署名单位: University System of Maryland; University of Maryland College Park
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/15-AOP1029
• 发表日期: 2016
• 页码: 2591-2642
• 关键词: diffusion; equation; noise

摘要

In this paper, we study the quasi-potential for a general class of damped semilinear stochastic wave equations. We show that as the density of the mass converges to zero, the infimum of the quasi-potential with respect to all possible velocities converges to the quasi-potential of the corresponding stochastic heat equation, that one obtains from the zero mass limit. This shows in particular that the Smoluchowski Kramers approximation is not only valid for small time, but in the zero noise limit regime, can be used to approximate long-time behaviors such as exit time and exit place from a basin of attraction.