Strong convergence rate in averaging principle for stochastic FitzHugh–Nagumo system with two time-scales

This article deals with averaging principle for stochastic FitzHugh–Nagumo system with different time-scales. Under suitable conditions, the existence of an averaging equation eliminating the fast variable for this coupled system is proved, and as a consequence, the system can be reduced to a single...

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Bibliographic Details
Published in:Journal of mathematical analysis and applications 2014-08, Vol.416 (2), p.609-628
Main Authors: Fu, Hongbo, Wan, Li, Wang, Youzhen, Liu, Jicheng
Format: Article
Language:English
Subjects:
Averaging principle
Invariant measure
Stochastic FitzHugh–Nagumo system
Strong convergence order
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Summary:This article deals with averaging principle for stochastic FitzHugh–Nagumo system with different time-scales. Under suitable conditions, the existence of an averaging equation eliminating the fast variable for this coupled system is proved, and as a consequence, the system can be reduced to a single stochastic ordinary equation with a modified coefficient. Moreover, the rate of convergence for the slow component towards the solution of the averaging equation is of order 1/2.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2014.02.062