Sentence examples for square convergence from inspiring English sources

Mean square convergence of the random Fourier series are discussed.

Note that the mean square convergence results stated in [12] relies on some strict assumptions.

In particular, we propose the asymptotic and per-step (mean square) convergence factors as measures of the convergence speed and derive the exact value for the per-step (mean square) convergence factor.

Then we study their performances in terms of the mean square convergence and the convergence in probability.

A random mean value theorem is established and the mean square convergence of these methods is proved.

As it was in the case of the mean convergence, a sufficient condition for mean square convergence is (39).

The strong and mean-square convergence rates are obtained.

The strong and mean-square convergence rates are explicitly obtained.

Fig. 7 Mean-square convergence of the splitting method.

Section 4 deals with the mean-square convergence, the almost surely convergence and the asymptotic normality of these estimators.

In what follows, we study the mean-square convergence of the estimator (hat{c}^{2} ) defined by (13).