By using moment inequality and truncated method,the Lp convergence and complete convergence for the general double index weighted partial sums was obtained,which improve the corresponding results of Q.

By the mean\'s moment inequality and truncated method, the author is able to give the Lp convergence of weighted sums sum from k=1 to n(ankXk), which extend the corresponding results in some previous papers.

Effect of calculation parameters on convergence speed of one-dimensional transient heat transfer series solution;

Study on convergence speed of high order P type iterative learning control algorithm;

Analysis of convergence speed of repetitive control system;

Improvement of convergence rates for the empirical Bayes test problem in scale exponential family;

Mean convergence rate of derivatives approximation by Lagrange interpolation operators;

Making use of the formula of and the inequality of,this paper has deduced two types of probabilistic approximation of C-semigroups and the estimating of convergent rate.

It has been shown that the convergent rate .

Then,using Taylor expansion of the semigroup,Holder s inequality and estimations of moment-generating functions of some suitable random variables,some briefly probabilistic approximations and estimations of convergent rates are obtained for C-semigroups.