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Strong convergence rate in averaging principle for stochastic FitzHugh-Nagumo system with two time-scales. (English) Zbl 1325.60107
Summary: This article deals with the averaging principle for a 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 $$1/2$$.

##### MSC:
 60H15 Stochastic partial differential equations (aspects of stochastic analysis) 60H10 Stochastic ordinary differential equations (aspects of stochastic analysis) 60F15 Strong limit theorems
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