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We prove a strong convergence rate of the averaging principle for general two-time-scales stochastic evolution equations driven by cylindrical Wiener processes. In particular, our general result can be used to deal with a large class of quasi-linear stochastic partial differential equations, such as stochastic reaction–diffusion equations, stochastic  p -Laplace equations, stochastic porous media equations, and so on.

Strong convergence rate of the averaging principle for a class of slow–fast stochastic evolution equations