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In this paper, we establish normalized and self-normalized Cram\'er-typemoderate deviations for Euler-Maruyama scheme for SDE. As a consequence of ourresults, Berry-Esseen's bounds and moderate deviation principles are alsoobtained. Our normalized Cram\'er-type moderate deviations refines the recentwork of [Lu, J., Tan, Y., Xu, L., 2022. Central limit theorem andself-normalized Cram\'er-type moderate deviation for Euler-Maruyama scheme.Bernoulli 28(2): 937--964].

Cram\'er-type moderate deviations for Euler-Maruyama scheme for SDE