LARGE DEVIATIONS THEORY FOR MARKOV JUMP MODELS OF CHEMICAL REACTION NETWORKS

• 成果类型: Article
• 署名作者: Agazzi, Andrea; Dembo, Amir; Eckmann, Jean-Pierre
• 署名单位: Stanford University; Stanford University; University of Geneva; University of Geneva; University of Geneva; Duke University
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/17-AAP1344
• 发表日期: 2018
• 页码: 1821-1855
• 关键词: global attractor conjecture; reaction systems; distributions

摘要

We prove a sample path Large Deviation Principle (LDP) for a class of jump processes whose rates are not uniformly Lipschitz continuous in phase space. Building on it, we further establish the corresponding Wentzell-Freidlin (W-F) (infinite time horizon) asymptotic theory. These results apply to jump Markov processes that model the dynamics of chemical reaction networks under mass action kinetics, on a microscopic scale. We provide natural sufficient topological conditions for the applicability of our LDP and W-F results. This then justifies the computation of nonequilibrium potential and exponential transition time estimates between different attractors in the large volume limit, for systems that are beyond the reach of standard chemical reaction network theory.