Normalized convergence of random variables

The properties of a new type of convergence of sequences of random variables are considered. Normalized convergence occupies an intermediate position between convergence in the mean and convergence in probability. It is relevant for studying the rate of convergence of stochastic iterative optimization algorithms and statistical methods of stochastic programming.Translated from Kibernetika i Sistemnyi Analiz, No. 3, pp. 84–92, May–June, 1992.