双随机狄里克莱级数在收敛半平面上的增长性

The growth of bi-random Dirichlet series on convergent half-plane

运用经典强大数定律 ,研究了随机变量序列 {Xn}在独立 (可不同分布 )情形下的性质 ,并得出在一定条件下 ,当双随机狄里克莱级数 ∑∞n =1anXn(ω)e-λn(ω)s 与∑∞n =1ane-Eλns 满足(ⅰ )limn→∞λnEλn=1且limn→∞nEλn=D <∞ ;(ⅱ )limn→∞ln｜an ｜Eλn=0时 。

Studied some properties of independent and not-equally distributed random variables {X n} by the classical strong law of large numbers. Under certain conditions, when ~{*'!F~}~{!^~}n=1a nX n(~{&X~})~{*+~}e~{*+~}~{*,*)~}-~{&K*-~}n(~{&X~})s~{***'~} and ~{*'!F~}~{!^~}n=1a n~{*+~}e~{*+*,*)~}-E~{&K*-~}ns~{***'~} satisfy: (~{'!~})~{*'*)*+~}lim~{*+**~}n~{!z!^~}~{&K*-~}nE~{&K*-~}n=1 and ~{*'*)*+~}lim~{*+**~}n~{!z!^~}nE~{&K*-~}n=D<~{!^~};~{*'*%~}(~{''~})~{*'*)*+~}lim~{*+**~}n~{!z!^~}~{*+~}ln~{*+~}|a n|E~{&K*-~}n=0.~{*'*$~}they have the same abscissa and the same order of growth.