经验过程的一般加权大数定律

Law of Large Numbers for General Weighted Empirical Processes

研究了经验过程中加权系数具有某些较弱性质的加权和收敛问题.利用经验过程中已有的几个概率不等式与一般加权和的对称化不等式,得到了经验过程中的独立同分布随机元序列的这类加权和的强、弱大数定律成立的充分条件(E‖f(X0)‖1/αG<∞).同时,对经验过程中的Cesaro大数定律和欧拉弱大数定律进行了推广.

Convergence for the weighted sums which weighting coefficients is provided with some weaker natures in empirical processes is investigated.With some probability inequalities and the symmetrization inequality for general weighted sums in empirical processes which have been obtained,the sufficient condition（E‖f（X0）‖1/αG∞） is obtained for the strong and weak law of large numbers of the weighted sums of a sequence of random elements that are independent and identically distributed in empirical processes.At the same time,the Cesaro law of large numbers and the Euler weak law of large numbers in empirical processes are spread.