Averaging principle for slow-fast stochastic differential equations with time dependent locally Lipschitz coefficients

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This paper is devoted to studying the averaging principle for stochastic differential equations with slow and fast time-scales, where the drift coefficients satisfy local Lipschitz conditions with respect to the slow and fast variables, and the coefficients in the slow equation depend on time t and ω. Making use of the techniques of time discretization and truncation, we prove that the slow component strongly converges to the solution of the corresponding averaged equation.