Abstract:

Under the conditions(without independence): (i) 9 > 0, such that sup
n1
E|Zn|
< +1, (ii) 9 > 0, such that sup
n1
E|Zn|− < +1, the random series
1P
n=1
anZne−ns and
series
1P
n=1
ane−ns a.s. have the same abscissa of convergence, the (R) order, lower order
and type.

Key words: Random Dirichlet series,  the order of growth, low order , convex regularization
type