The Growth Of B-value Of Random Dirichlet Series

This paper mainly use the growth of Random Dirichlet Series in both convergence whole plane and convergence half-plane to research the growth of Random Dirichlet Series in both convergence whole plane and convergence half-plane in Branch space under sequence of random variables not meeting independent and identical distribution. This paper is divided into three parts:In the first part, introduced the background, Random Dirichlet Series and the result of the growth of Random Dirichlet Series in both convergence whole plane and convergence half-plane. In the second part, using the following conditions:(1)If theXn(ω) satisfy the condition that a plural α,(?) α>0could lead to sup{E|Xn-α|α}<∞, n≥1(2)If the Xn(ω) satisfy the condition that a plural α,(?) β>0could lead to sup{E|Xn-α|-β}<∞, n>1Discussing to get:B-valued Random Dirichlet Serise and B-Dirichlet Series have the same abscissa of convergence、level and type.(B is Branch space, is Probability space (), of complex random variable).In the third part, under the condition of part two, discussing the growth of Random Dirichlet Series in convergence half-plane and getting some necessary and sufficient conditions for Zero-oder B-valued Random Dirichlet Serise,having the same conclu-sion with the second part in convergence half-plane.