The Annals of Applied Probability
- Ann. Appl. Probab.
- Volume 24, Number 2 (2014), 721-759.
Central limit theorems and diffusion approximations for multiscale Markov chain models
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.
Ann. Appl. Probab., Volume 24, Number 2 (2014), 721-759.
First available in Project Euclid: 10 March 2014
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Primary: 60F05: Central limit and other weak theorems 92C45: Kinetics in biochemical problems (pharmacokinetics, enzyme kinetics, etc.) [See also 80A30] 92C37: Cell biology 80A30: Chemical kinetics [See also 76V05, 92C45, 92E20] 60F17: Functional limit theorems; invariance principles 60J27: Continuous-time Markov processes on discrete state spaces 60J28: Applications of continuous-time Markov processes on discrete state spaces 60J60: Diffusion processes [See also 58J65]
Kang, Hye-Won; Kurtz, Thomas G.; Popovic, Lea. Central limit theorems and diffusion approximations for multiscale Markov chain models. Ann. Appl. Probab. 24 (2014), no. 2, 721--759. doi:10.1214/13-AAP934. https://projecteuclid.org/euclid.aoap/1394465370