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We consider the long-time behavior of an explicit tamed Euler scheme appliedto a class of stochastic differential equations driven by additive noise, undera one-sided Lipschitz continuity condition. The setting encompasses driftnonlinearities with polynomial growth. First, we prove that moment bounds forthe numerical scheme hold, with at most polynomial dependence with respect tothe time horizon. Second, we apply this result to obtain error estimates, inthe weak sense, in terms of the time-step size and of the time horizon, toquantify the error to approximate averages with respect to the invariantdistribution of the continuous-time process. We justify the efficiency of usingthe explicit tamed Euler scheme to approximate the invariant distribution,since the computational cost does not suffer from the at most polynomial growthof the moment bounds. To the best of our knowledge, this is the first result inthe literature concerning the approximation of the invariant distribution forSDEs with non-globally Lipschitz coefficients using an explicit tamed scheme.

Approximation of the invariant distribution for a class of ergodic SDEs  with one-sided Lipschitz continuous drift coefficient using an explicit tamed  Euler scheme