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A Functional Central Limit Theorem for the Becker-Döring model

Wen Sun 1
1 MAMBA - Modelling and Analysis for Medical and Biological Applications
Inria de Paris, LJLL (UMR_7598) - Laboratoire Jacques-Louis Lions
Abstract : We investigate the fluctuations of the stochastic Becker-D\"oring model of polymerization when the initial size of the system converges to infinity. A functional central limit problem is proved for the vector of the number of polymers of a given size. It is shown that the stochastic process associated to fluctuations is converging to the strong solution of an infinite dimensional stochastic differential equation (SDE) in a Hilbert space. We also prove that, at equilibrium, the solution of this SDE is a Gaussian process. The proofs are based on a specific representation of the evolution equations, the introduction of a convenient Hilbert space and several technical estimates to control the fluctuations, especially of the first coordinate which interacts with all components of the infinite dimensional vector representing the state of the process.
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Submitted on : Friday, October 13, 2017 - 9:06:44 AM
Last modification on : Friday, January 21, 2022 - 3:13:50 AM

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Wen Sun. A Functional Central Limit Theorem for the Becker-Döring model. Journal of Statistical Physics, Springer Verlag, 2018, 171 (1), pp.145-165. ⟨10.1007/s10955-018-1993-1⟩. ⟨hal-01616039⟩



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