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作者：Schlather, M
作者单位：Lancaster University
摘要：This paper aims to combine the central limit theorem with the limit theorems in extreme value theory through a parametrized class of limit theorems where the former ones appear as special cases. To this end the limit distributions of suitably centered and normalized l(cp(n))-norms of n-vectors of positive i.i.d. random variables are investigated. Here, c is a positive constant and p(n) is a sequence of positive numbers that is given intrinsically by the form of the upper tail behavior of the r...
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作者：Giné, E; Kwapien, S; Latala, R; Zinn, J
作者单位：University of Connecticut; University of Connecticut; University of Warsaw; Texas A&M University System; Texas A&M University College Station
摘要：Let X, X-i, i epsilon N, be independent identically distributed random variables and let h(x, y) = h(y, x) be a measurable function of two variables. It is shown that the bounded law of the iterated logarithm, lim sup(n) log n(log n)(-1) \ Sigma1 less than or equal toi . \ \g \ \ (infinity) < infinity) less than or equal to C.
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作者：Hitczenko, P; Montgomery-Smith, S
作者单位：Drexel University; University of Missouri System; University of Missouri Columbia
摘要：This paper considers how to measure the magnitude of the sum of independent random variables in several ways. We give a formula for the tail distribution for sequences that satisfy the so called Levy property. We then give a connection between the tail distribution and the pth moment, and between the pth moment and the rearrangement invariant norms.
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作者：Seidenfeld, T; Schervish, MJ; Kadane, JB
作者单位：Carnegie Mellon University; Carnegie Mellon University
摘要：Improper regular conditional distributions (red's) given a sigma-field A have the following anomalous property. For sets A is an element of A, Pr(A \ A) is not always equal to the indicator of A. Such a property makes the conditional probability puzzling as a representation of uncertainty. When red's exist and the sigma-field,A is countably generated, then almost surely the red is proper. We give sufficient conditions for an red to be improper in a maximal sense, and show that these conditions...
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作者：Brown, TC; Xia, AH
作者单位：University of Melbourne
摘要：Barbour introduced a probabilistic view of Stein's method for estimating the error in probability approximations. However, in the case of approximations by general distributions on the integers, there have been no purely probabilistic proofs of Stein bounds till this paper. Furthermore, the methods introduced here apply to a very large class of approximating distributions on the non-negative integers, among which there is a natural class for higher-order approximations by probability distribut...
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作者：Chi, ZY
作者单位：University of Chicago
摘要：Given two Polish spaces A(X) and A(Y), let rho : A(X) x A(Y) --> R-d be a bounded measurable function. Let X = {X-n : n greater than or equal to 1) and Y = {Y-n: n greater than or equal to 1} be two independent stationary processes on A(X)(infinity) and A(Y)(infinity), respectively. The article studies the large deviation principle (LDP) for n(-1) Sigma(k=1)(n) rho(X-k, Y-k), conditional on X. Based on a stochastic version of approximate subadditivity, it is shown that if Y satisfies certain m...
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作者：Bryc, W
作者单位：University System of Ohio; University of Cincinnati
摘要：We analyze and identify stationary fields with linear regressions and quadratic conditional variances. We give sufficient conditions to determine one-dimensional distributions uniquely as normal and as certain compactly supported distributions. Our technique relies on orthogonal polynomials, which under our assumptions turn out to be a version of the so-called continuous q-Hermite polynomials.
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作者：Einmahl, U; Kuelbs, J
作者单位：Universite Libre de Bruxelles; University of Wisconsin System; University of Wisconsin Madison
摘要：We identify the possible cluster sets for a general law of the iterated logarithm in the Banach space setting, and show that all the possible limit sets arise as cluster sets for some random vector in an arbitrary separable Banach space. This extends previous results obtained in finite dimensional Euclidean spaces.
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作者：Holroyd, AE; Liggett, TM
作者单位：University of California System; University of California Los Angeles
摘要：We consider the following problem: given an i.i.d. family of Bernoulli random variables indexed by Z(d), find a random occupied site X is an element of Z(d) such that relative to X, the other random variables are still i.i.d. Bernoulli. Results of Thorisson imply that such an X exists for all d. Liggett proved that for d = 1, there exists an X with tails P(\X\ greater than or equal to t) of order ct(-1/2), but none with finite 1/2th moment. We prove that for general d there exists a solution w...
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作者：Huang, YC; Dudley, RM
作者单位：Massachusetts Institute of Technology (MIT)
摘要：Let F be any distribution function on R, and F-n be the nth empirical distribution function based on variables i.i.d. (F). It is shown that for 2 < p < infinity and a constant C(p) < infinity, not depending on F, on some probability space there exist Fn and Brownian bridges B-n such that for the Wiener-Young p-variation norm parallel to . parallel to([p]), Eparallel ton(1/2)(F-n - F) - B-n o Fparallel to([P]) less than or equal to C(p)n((2-p)/(2p)), where (B-n o F)(x) = B-n(F(x)). The expectat...
