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Abstract This paper deals with averaging principle for two-time-scale stochastic differential equations (SDEs) with non-Lipschitz coefficients, which extends the existing results: from Lipschitz to non-Lipschitz case. Under suitable conditions, the existence of an averaging equation eliminating the fast variable for coupled system is established, and as a result, the system can be reduced to a single SDEs with a modified coefficient which is also non-Lipschitz. Moreover, it is shown that the slow variable strongly converges to the solution of the corresponding averaging equation. [ABSTRACT FROM AUTHOR]

This article deals with the weak error in averaging principle for a stochastic wave equation on a bounded interval [ 0 , L ] , perturbed by an oscillating term arising as the solution of a stochastic reaction–diffusion equation evolving on the fast time scale. Under suitable conditions, it is proved that the rate of weak convergence of the original solution to the solution of the corresponding averaged equation is of order 1 via an asymptotic expansion approach. [ABSTRACT FROM AUTHOR]

This article deals with averaging principle for stochastic hyperbolic–parabolic equations with slow and fast time-scales. Under suitable conditions, the existence of an averaging equation eliminating the fast variable for this coupled system is proved. As a consequence, an effective dynamics for slow variable which takes the form of stochastic wave equation is derived. Also, the rate of strong convergence for the slow component towards the solution of the averaging equation is obtained as a byproduct. [ABSTRACT FROM AUTHOR]

Abstract: 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. [Copyright &y& Elsevier]