Acta mathematica scientia,Series B ›› 1991, Vol. 11 ›› Issue (4): 463-469.
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Sun Daochun
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Abstract: 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.
Sun Daochun. THE NATURAL BOUNDARY OF SOME RANDOM POWER SERIES[J].Acta mathematica scientia,Series B, 1991, 11(4): 463-469.
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