Abstract
A new concept of (normalized) convergence of random variables is introduced. This convergence is preserved under Lipschitz transformations, follows from convergence in mean and itself implies convergence in probability. If a sequence of random variables satisfies a limit theorem then it is a normalized convergent sequence. The introduced concept is applied to the convergence rate study of a statistical approach in stochastic optimization.
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Ermoliev, Y.M., Norkin, V.I. Normalized convergence in stochastic optimization. Ann Oper Res 30, 187–198 (1991). https://doi.org/10.1007/BF02204816
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DOI: https://doi.org/10.1007/BF02204816