随机三角级数收敛性与Paley-Zygmund定理的推广

Convergence of Random Triangular Series and Promotion of the Paley-Zygmund Theorem

利用Beppo-Levi定理和Hlder不等式,以及Minkowski不等式研究了随机级数∑∞n=1X2n的收敛性,其中{Xn}是随机变量序列,在此基础上讨论了随机级数∑∞n=1an Xn的收敛性,其中{Xn}为正项同分布随机变量序列。将Paley-Zygmund定理推广到更一般的情形。

Convergence of random series ∑∞ n=1X2n was studied by Beppo-Levi theorem,Hlder inequality and Minkowski inequality,where {Xn} is the random variables.And convergence of the random series ∑∞ n=1anXn was then discussed,where {Xn} is the same distribution random variables.Then the Paley-Zygmund theorem was generalized.