A universal form of the Chung-type law of the iterated logarithm
نویسندگان
چکیده
منابع مشابه
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چکیده ندارد.
On the law of the iterated logarithm.
The law of the iterated logarithm provides a family of bounds all of the same order such that with probability one only finitely many partial sums of a sequence of independent and identically distributed random variables exceed some members of the family, while for others infinitely many do so. In the former case, the total number of such excesses has therefore a proper probability distribution...
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ABSTRACT Let 0 < α ≤ 2 and - ∞ <β <∞. Let {X n ;n ≥ 1} be a sequence of independent copies of a real-valued random variable X and set S n = X 1+⋯+X n , n ≥ 1. We say X satisfies the (α,β)-Chover-type law of the iterated logarithm (and write X∈C T L I L(α,β)) if [Formula: see text] almost surely. This paper is devoted to a characterization of X ∈C T L I L(α,β). We obtain sets of necessary and su...
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ژورنال
عنوان ژورنال: The Annals of Probability
سال: 1997
ISSN: 0091-1798
DOI: 10.1214/aop/1023481104