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.

Key words: Dirichlet series, B-valued Bi-random Dirichlet series; The strong law of large numbers, Independence, Abscissa of convergence