期刊
ANNALS OF APPLIED PROBABILITY
卷 24, 期 2, 页码 721-759出版社
INST MATHEMATICAL STATISTICS
DOI: 10.1214/13-AAP934
关键词
Reaction networks; central limit theorem; martingale methods; Markov chains; scaling limits
资金
- NSF FRG [DMS 05-53687]
- NSF [DMS 11-06424]
- NSERC
- Division Of Mathematical Sciences
- Direct For Mathematical & Physical Scien [1106424] Funding Source: National Science Foundation
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.
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