Average and deviation for the stochastic FitzHugh--Nagumo system

Wei Wang, A. J. Roberts


An averaged system for the slow-fast stochastic FitzHugh--Nagumo system is derived in this paper. The rate of convergence in probability is obtained as a byproduct. Moreover the deviation between the original system and the averaged system is studied. A martingale approach proves that the deviation is described by a Gaussian process. The deviation gives a more accurate asymptotic approximation than previous work.

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DOI: http://dx.doi.org/10.21914/anziamj.v50i0.1391

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