For SDEs with superlinearly growing drift and non-degenerate multiplicative noise, the variable-step tamed Euler-Maruyama scheme converges uniformly in time at rate O(eta_n^alpha) in Wasserstein and total variation distance, for any alpha in (0,1/2).
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Tamed Euler-Maruyama method for SDEs with non-globally Lipschitz drift and multiplicative noise
For SDEs with superlinearly growing drift and non-degenerate multiplicative noise, the variable-step tamed Euler-Maruyama scheme converges uniformly in time at rate O(eta_n^alpha) in Wasserstein and total variation distance, for any alpha in (0,1/2).