CHUNG-TYPE LAW OF THE ITERATED LOGARITHM OF l∞-VALUED GAUSSIAN 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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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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چکیده ندارد.
The Law of the Iterated Logarithm and Marcinkiewicz Law of Large Numbers for B-Valued U-Statistics 1
Suppose that B is a separable Banach space and (S, 6 a, P) a probability space. H is a measurable symmetric kernel function from S" into B. In this paper we shall further study some limit theorems for B-valued U-statistics U",,H based on P and H. Special attention is paid upon the Marcinkiewicz type law of large numbers and the law of the iterated logarithm. Our results can be regarded as exten...
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ژورنال
عنوان ژورنال: Journal of the Korean Mathematical Society
سال: 2009
ISSN: 0304-9914
DOI: 10.4134/jkms.2009.46.2.347