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作者：Ho, HC; Hsing, T
作者单位：Academia Sinica - Taiwan; Texas A&M University System; Texas A&M University College Station
摘要：Let X-n = Sigma(i=1)(infinity) alpha(i) epsilon(n-i), where the epsilon(i) are i.i.d. with mean 0 and finite second moment and the ai are either summable or regularly varying with index epsilon (- 1, - 1/2). The sequence {X-n} has short memory in the former case and long memory in the latter. For a large class of functions K, a new approach is proposed to develop both central (root n rate) and noncentral (non-root n rate) limit theorems for S-N = Sigma(n=1)(N) [K(X-n) - EK(X-n)]. Specifically,...
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作者：Gine, E; Gotze, F; Mason, DM
作者单位：University of Connecticut; University of Connecticut; University of Bielefeld; University of Delaware
摘要：Let X, X-i, i is an element of N, be independent, identically distributed random variables. It is shown that the Student t-statistic based upon the sample {X-i}(i less than or equal to 1)(n) is asymptotically N(0, 1) if and only if X is in the domain of attraction of the normal law. It is also shown that, for any X, if the self-normalized sums U-n := Sigma(i=1)(n) X-i/(Sigma(i=1)(n) X-i(2))(1/2), n is an element of N, are stochastically bounded then they are uniformly subgaussian that is, sup(...
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作者：Leuridan, C
作者单位：Communaute Universite Grenoble Alpes; Universite Grenoble Alpes (UGA); Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
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作者：Voit, M
作者单位：Eberhard Karls University of Tubingen
摘要：In this paper we prove central limit theorems of the following kind: let S-d subset of Rd+1 be the unit sphere of dimension d greater than or equal to 2 with uniform distribution omega(d). For each k is an element of N, consider the isotropic random walk (X-n(k))(n greater than or equal to 0) on S-d starting at th north pole with jumps of fixed sizes angle(X-n(k), X-n-1(k)) = pi/root k for all n greater than or equal to 1. Then there is some k(0)(d) such that for all k greater than or equal to...
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作者：Darling, RWR; Pardoux, E
作者单位：State University System of Florida; University of South Florida; Aix-Marseille Universite
摘要：Suppose {T-t} is the filtration induced by a Wiener process W in R-d, tau is a finite {T-t} stopping time (terminal time), xi is an T-tau-measurable random variable in R-k (terminal value) and f(., y, z) is a coefficient process, depending on y is an element of R-k and z is an element of L(R-d; R-k), satisfying (y - (y) over bar) [f(s, y, z) - f(s, (y) over bar, z)] less than or equal to -a/y - (y) over bar/(2) (f need not be Lipschitz in Y), and /f(s, y, z) -f(s, y (z) over bar/ less than or ...
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作者：Dembo, A
作者单位：Stanford University; Stanford University
摘要：We derive inequalities of the form Delta(P, Q) less than or equal to H(P\R) + H(Q\R) which hold for every choice of probability measures P, Q, R, where H(P\R) denotes the relative entropy of P with respect to R acid Delta(P, Q) stands for a coupling type distance between P and Q. Using the chain rule for relative entropies and then specializing to Q with a given support we recover some of Talagrand's concentration of measure inequalities for product spaces.
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作者：de Fitte, PR
作者单位：Universite de Rouen Normandie
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作者：Bai, ZD
作者单位：National Sun Yat Sen University
摘要：It was conjectured in the early 1950's that the empirical spectral distribution of an n x n matrix, of lid entries, normalized by a factor of 1/root n, converges to the uniform distribution over the unit disc on the complex plane, which is called the circular law. Only a special case of the conjecture, where the entries of the matrix are standard complex Gaussian, is known. In this paper, this conjecture is proved under the existence of the sixth moment and some smoothness conditions. Some ext...
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作者：Kesten, H
作者单位：Cornell University
摘要：Let {X-i}(i greater than or equal to 1) be i.i.d. random variables with common distribution function F-1 and let S-n = Sigma(1)(n) X-i. We find a necessary and sufficient condition (directly in terms of Fl for the existence of sequences of constants (a,) and {beta(n)} with beta(n) up arrow infinity such that 0 < lim inf beta(n)(-1) max(j less than or equal to n) /S-j-alpha(j)/ < infinity w.p.1., and such that for any choice of <(alpha)over tilde>(n), it hold w.p.1 that lim inf beta(n)(-1) max(...
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作者：Wang, FY
作者单位：Beijing Normal University; University of Warwick
摘要：By using logarithmic transformations, an explicit lower bound estimate of heat kernels is obtained for diffusion processes on Riemannian manifolds. This estimate is sharp for both short and long times, especially for heat kernels on a compact manifold, and is extended to manifolds with unbounded curvature.
