二重B-值随机Dirichlet级数的线性增长性

THE LINEAR GROWTH OF THE DOUBLE B-VALUED RANDOM DIRICHLET SERIES

本文研究了二重B-值随机Dirichlet级数线性增长性的问题.利用二重B-值随机变量列{Xmn}在某阶矩一致有界条件下的性质和Paley-Zygmund不等式,并结合二重Dirichlet级数的成果,获得了在一定条件下,二重B-值随机Dirichlet级数a.s.必然与二重Dirichlet级数有相同的线性增长性,推广了二重Dirichlet级数的线性增长性.

In this paper,we study the linear growth of the double B-valued random Dirichlet series.Using the properties of a double sequence of B-valued random variable with some uniform bounded moments and Paley-Zygmund inequality,we obtain,under suitable conditions,the double B-valued random Dirichlet series has a.s.the same linear growth as the double Dirichlet series,which extend the linear growth of the double Dirichlet series.