Final Report: 3.4.1 Rare Events, Control and Metastability of Weakly Interacting Particle Systems
Technical Report,31 May 2012,30 May 2016
Brown University Providence United States
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Many engineering systems can be modeled as a large collection of stochastically evolving particles, whose dynamics are weakly coupled by an interaction that depends only on the empirical distribution of the particles. Good design of these systems requires accurate estimation of key performance measures of interest, such as the expected exit time from the neighborhood of a desirable operating point. This requires an understanding of stability, mestastability and other related aspects of the long-time behavior of the system. The focus of this proposal is to develop general analytical and computational methods for quantitative characterizations of these properties. The techniques developed will include partial differential equation characterizations and control representations for the construction of Lyapunov functions, formulation and solution of optimization problems that identify the most likely large way in which certain rare events of interest occur and the development of efficient importance sampling algorithms for accurate estimation the probabilities of rare events of interest. Additionally, these methods developed will be applied to shed insight into the performance and design of real-world systems.
- Statistics and Probability