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Convergence of B-valued Bi-random Dirichlet Series
B -值双随机Dirichlet级数的收敛性

Keywords: Dirichlet serieszz,B-valued Bi-random Dirichlet series, ,The strong law of large numberszz,Independencezz,Abscissa of convergencezz
Dirichlet级数
,B,-值双随机Dirichlet级数,强大数定律,收敛横坐标

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Abstract:

By studying the convergence of B-valued Bi-random Dirichlet series under the following conditions: (i) {X_n(\omega)} satisfying the strong law of large numbers and 0<\mathop{\underline{\lim}}\limits_{n\to\infty}\Big\|\frac{\sum\limits_{i=1}^nEX_i}{n}\Big\| \leq\mathop{\overline{\lim}}\limits_{n\to\infty}\Big\|\frac{\sum\limits_{i=1}^nEX_i}{n}\Big\|<+\infty. (ii){X_{n}}is independent and unequally distributed and \mathop{\underline{\lim}}\limits_{n\to\infty}E||X_n||>0,\quad \sup\limits_{n\geq 1}E||X_n||^p <+\infty\quad (p>1),some simple and explicit formulae of the absciassa of convergence are obtained.

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