经验过程的欧拉强大数定律

Euler Strong Law of Large Numbers for Empirical Processes

利用经验过程中已有的概率不等式及欧拉加权系数的性质,研究经验过程中独立同分布随机元序列的欧拉可求和性,得到了经验过程欧拉强大数定律成立的充分条件(E‖f(X0)‖G2<∞).在相同条件下,将经验过程中的欧拉弱大数定律推广到强收敛情形.

With the probability inequality obtained in empirical processes and nature of the Euler weighting coefficients, the Euler summability of a sequence of random elements independent and identically distributed in empirical processes was investigated. The sufficient condition （E｜｜f（X0）｜｜＆^2〈∞） is obtained for the Euler strong law of large numbers in empirical processes. Under identical conditions, the Euler weak law of large numbers in empirical processes was spread to the situation of strong convergence.