1.10. Let {Xn, n E N} be a sequence of independent, identically distributed r.v.'s with {(IXI /)...

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1.10. Let {Xn, n E N} be a sequence of independent, identically distributed r.v.'s with {(IXI /) < 00; and Sn = 2:j=1 Xj . Define a = inf{n ~ 1: IXnl >

n}. Prove that if J((ISal/a)l(an Cn = IT 9J{IXj l ::s j} ~ C>O;
j=1 00 11 L -ISn-ll dgP < 00.]
11=1 n (a=n)
9.S APPLICATIONS I 373

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