The Annals of Applied Probability

Central limit theorems and diffusion approximations for multiscale Markov chain models

Hye-Won Kang, Thomas G. Kurtz, and Lea Popovic

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Abstract

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.

Article information

Source
Ann. Appl. Probab., Volume 24, Number 2 (2014), 721-759.

Dates
First available in Project Euclid: 10 March 2014

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1394465370

Digital Object Identifier
doi:10.1214/13-AAP934

Mathematical Reviews number (MathSciNet)
MR3178496

Zentralblatt MATH identifier
1319.60045

Subjects
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]

Keywords
Reaction networks central limit theorem martingale methods Markov chains scaling limits

Citation

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


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