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作者：GRIFFIN, PS; MCCONNELL, TR
摘要：Let T-r be the first time a sum S-n of nondegenerate i.i.d. random vectors in R(d) leaves the sphere of radius r in some given norm. We characterize, in terms of the distribution of the individual summands, the following probabilistic behavior: S-Tr/parallel to S(Tr)parallel to has no subsequential weak limit supported on a closed half-space. In one dimension, this result solves a very general form of the gambler's ruin problem. We also characterize the existence of degenerate limits and obtai...
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作者：TALAGRAND, M
作者单位：University System of Ohio; Ohio State University
摘要：Consider the product measure mu(p) on {0, 1}(n), when 0 (resp. 1) is given weight 1 - p (resp, p). Consider a monotone subset A of {0, 1}(n). We give a precise quantitative form to the following statement: if A does not depend much on any given coordinate, d mu(p)(A)/dp is large. Thus, in that case, there is a threshold effect and mu(p)(A) jumps from near 0 to near 1 in a small interval.
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作者：GINE, E; ZINN, J
作者单位：Texas A&M University System; Texas A&M University College Station
摘要：It is proved that, for h measurable and symmetric in its arguments and X(i) i.i.d., if the sequence (n(-m/2)SIGMA(i1,...,im less-than-or-equal-to n, ij not-equal ik if j not-equal k) h(X(i1),...,X(im))}n=1infinity is stochastically bounded, then Eh2 < infinity and Eh(X1,x2,...,x(m)) = 0 a.s..
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作者：MAJOR, P
摘要：We prove limit theorems for weighted U-statistics and express the limit by means of multiple stochastic integrals. This is a generalization of the paper by O'Neil and Redner. In that paper the method of moments was applied which does not work in the general case. Hence we had to work out a different method. In particular, in Theorem 4 we describe the limit of a model proposed by O'Neil and Redner. In this model the weight functions cause an intricate cancellation, and the limit can be presente...
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作者：BETZ, C; GZYL, H
摘要：By using an appropriate martingale, we compute the joint distribution of the hitting time and place of a sphere by d-dimensional Brownian motion, when the process starts outside the sphere.
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作者：ROSENTHAL, JS
摘要：We analyze a random walk on the orthogonal group SO(N) given by repeatedly rotating by a fixed angle through randomly chosen planes of R(N). We derive estimates of the rate at which this random walk will converge to Haar measure on SO(N), using character theory and the upper bound lemma of Diaconis and Shashahani. In some cases we are able to establish the existence of a ''cut off phenomenon'' for the random walk. This is the first such non-trivial result on a nonfinite group.
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作者：GOEL, PK; HALL, P
作者单位：Australian National University
摘要：For a sequence of bivariate pairs (X(i), Y(i)), the concomitant Y[i] of the ith largest x-value X(i) equals that value of Y paired with X(i). In assessing the quality of a file-merging or file-matching procedure, the penalty for incorrect matching may often be expressed as the average value of a function of the difference Y[i] - Y(i). We establish strong laws and central limit theorems for such quantities. Our proof is based on the observation that if G(x)(.) denotes the distribution function ...
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作者：ALBIN, JMP
作者单位：Lund University; Chalmers University of Technology
摘要：We give a complete and rather explicit characterization of the upper and lower classes for a family of stationary Gaussian stochastic processes.
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作者：CHEN, HN
摘要：We continue our study on the stability properties of a population growth model with sexual reproduction on Z(d), d greater than or equal to 2. In the author's previous work, it was proved that in the type IV process (the two-dimensional symmetric model on Z(2)), the vacant state empty set is stable under perturbation of the initial state (the first kind of perturbation), and it is unstable under perturbation of the birth rate (the second kind of perturbation). In this paper we prove that in th...
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作者：TALAGRAND, M
作者单位：University System of Ohio; Ohio State University
摘要：Consider two independent sequences (X(i))i less-than-or-equal-to n and (X(i)')i less-than-or-equal-to n that are independent and uniformly distributed over [0, 1]d, d greater-than-or-equal-to 3. Under mild regularity conditions, we describe the convex functions phi such that, with large probability, there exists a one-to-one map pi from {1, ..., n} to {1, ..., n} for which [GRAPHICS] where K(p) depends on phi only
