数学物理学报(英文版) ›› 1991, Vol. 11 ›› Issue (4): 463-469.
孙道椿
Sun Daochun
摘要： Suppose that {Xn(ω)} are independent random complex variable sequence, E(Xn)=0 and limn→∞n√σn+1=(1)/ρ(V(Xn=σn2)) If ∃s>0 such that ∀F(H)>1-ε, we have
infn>1{∫H(|Xn(w)|2)/σn2F(dw)}>(1)/2. Then the circle {|Z|=ρ} is almost surely a natural boundary of the random series Σn=1∞ Xn(ω)Zn-1.