Article ID: | iaor19912122 |
Country: | Switzerland |
Volume: | 30 |
Start Page Number: | 187 |
End Page Number: | 198 |
Publication Date: | Mar 1991 |
Journal: | Annals of Operations Research |
Authors: | Ermoliev Yuri M., Norkin Valdimir I. |
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.