Asymptotics in the law of the iterated logarithm
نویسندگان
چکیده
منابع مشابه
Precise Asymptotics in Chung’s law of the iterated logarithm∗
Let X, X1, X2, . . . be i.i.d. random variables with mean zero and positive, finite variance σ2, and set Sn = X1 + . . . + Xn, n ≥ 1. We prove that, if EX2I{|X| ≥ t} = o((log log t)−1) as t →∞, then for any a > −1 and b > −1, lim 2↗1/√1+a ( 1 √ 1+a − 2)b+1 ∞n=1 (log n) a(log log n)b n P { maxk≤n |Sk| ≤ √ σ2π2n 8 log log n(2 + an) } = 4 π ( 1 2(1+a)3/2 )b+1Γ(b + 1), whenever an = o(1/ log log n).
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ژورنال
عنوان ژورنال: Теория вероятностей и ее применения
سال: 2008
ISSN: 0040-361X
DOI: 10.4213/tvp2470