The Law of the Iterated Logarithm for a Triangular Array of Empirical Processes
نویسندگان
چکیده
منابع مشابه
Law of the Iterated Logarithm for Stationary Processes
There has been recent interest in the conditional central limit question for (strictly) stationary, ergodic processes · · ·X−1, X0, X1, · · · whose partial sums Sn = X1 + · · · + Xn are of the form Sn = Mn+Rn, where Mn is a square integrable martingale with stationary increments and Rn is a remainder term for which E(R 2 n) = o(n). Here we explore the Law of the Iterated Logarithm (LIL) for the...
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15 صفحه اولOn 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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ژورنال
عنوان ژورنال: Electronic Journal of Probability
سال: 1997
ISSN: 1083-6489
DOI: 10.1214/ejp.v2-19