CENTRAL LIMIT THEOREMS AND DIFFUSION APPROXIMATIONS FOR MULTISCALE MARKOV CHAIN MODELS

• 成果类型: Article
• 署名作者: Kang, Hye-Won; Kurtz, Thomas G.; Popovic, Lea
• 署名单位: University System of Ohio; Ohio State University; University of Wisconsin System; University of Wisconsin Madison; University of Wisconsin System; University of Wisconsin Madison; Concordia University - Canada
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/13-AAP934
• 发表日期: 2014
• 页码: 721-759
• 关键词: reaction networks; Poisson equation; time-scales; martingales; kinetics

摘要

Ordinary differential equations obtained as limits of Markov processes appear in many settings. They may arise by scaling large systems, or by averaging rapidly fluctuating systems, or in systems involving multiple time-scales, by a combination of the two. Motivated by models with multiple time-scales arising in systems biology, we present a general approach to proving a central limit theorem capturing the fluctuations of the original model around the deterministic limit. The central limit theorem provides a method for deriving an appropriate diffusion (Langevin) approximation.