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 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.