系数为φ-混合序列的Dirichlet级数的增长性

Growth of stochastic Dirichlet series whose coefficient is φ-mixed series

利用φ-混合序列推广的Borel-Cantelli引理及一些收敛定理,在条件EXn=0,α>0,0<2α2nσ=2αE|Xn|2≤E2|Xn|<∞下,研究系数为φ-混合序列的随机Dirichlet级数∞∑n=0Xn(ω)e-λns的增长性,得出其增长级和非随机Dirichlet级数的增长级有类似的性质。

When EXn = 0, make it so that α 〉 0,0 〈 α^2σn^2 = α^2 E ｜ Xn｜^ 2≤ E^2 ｜ Xn｜〈 ∞. Under this condition, the growth of ∑n=0^∞ Xn（ω）e^-λn^5, a stochastic Dirichlet series whose coefficient is φ-mixed series, is studied by means of the extended Borel-Cantelli lemma and other limit theorems on mixed series. It is found that the stochastic Dirichlet series share common features with the non-random Dirichlet series in order of growth.