一类随机变量序列加权和的强大数定律

The strong law of large numbers for weighted sums of some random variables

研究一类被随机控制的随机变量序列加权和的Marcinkiewicz-Zygmund型强大数定律.在满足Rosenthal型不等式的情况下得到了比经典Marchinkiewicz-Zygmund型强大数定律稍强的大数定律,并将所得结论推广到了更为广泛的一类随机变量序列上.

A class of stochastically dominated Marcinkiewicz-Zygmund type strong law of large numbers for weighted sums of random variable is studied.Under the condition of satisfying Rosenthal type inequality,a law of large numbers which is slightly stronger than the classical Marchinkiewicz-Zygmund type strong law of large numbers is obtained,and the obtained results is extended to a wider class of random variable sequences.