Convergence rate of synchronization of systems with additive noise

Shahad Al-azzawi; Jicheng Liu; Xianming Liu

doi:10.3934/dcdsb.2017012

Article Contents

2017, Volume 22, Issue 2: 227-245. Doi: 10.3934/dcdsb.2017012

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Convergence rate of synchronization of systems with additive noise

School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan, Hubei 430074, China

* Corresponding author: Jicheng Liu
* Corresponding author: Jicheng Liu

Received: December 31, 2015

Revised: August 31, 2016

Published: December 2017

The first author is supported by NSF grants of China Nos. 11271013 and 11471340.

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Abstract

The synchronization of stochastic differential equations (SDEs) with additive noise is investigated in pathwise sense, moreover convergence rate of synchronization is obtained. The optimality of the convergence rate is illustrated through examples.

Keywords:

Synchronization,
random attractor,
one-sided Lipschitz dissipative condition,
exponential martingale inequality,
time-changed Brownian motion,
the law of the iterated logarithm.

Mathematics Subject Classification: Primary:60H10;Secondary:34F05.

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