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作者：CHENG, R
摘要：It is shown that a regular stationary random field on Z2 exhibits the weak (strong) commutation property if and only if its spectral density is the squared modulus of a weakly (strongly) outer function in the Hardy space H-2(T2) of the torus. Applications to prediction are discussed.
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作者：BAI, ZD; YIN, YQ
作者单位：University of Massachusetts System; University of Massachusetts Lowell
摘要：In this paper, the authors show that the smallest (if p less-than-or-equal-to n) or the (p - n + 1)-th smallest (if p > n) eigenvalue of a sample covariance matrix of the form (1/n)XX' tends almost surely to the limit (1 - square-root y)2 as n and p/n --> y is-an-element-of (0, infinity), where X is a p x n matrix with iid entries with mean zero, variance 1 and fourth moment finite. Also, as a by-product, it is shown that the almost sure limit of the largest eigenvalue is (1 + square-root y)2,...
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作者：BERKES, I; DEHLING, H
作者单位：University of Groningen
摘要：Motivated by recent results on pathwise central limit theorems, we study in a systematic way log-average versions of classical limit theorems. For partial sums S(k) of independent r.v.'s we prove under mild technical conditions that (1/log N)SIGMA(k less-than-or-equal-to N)(1/k)I{S(k)/a(k) is-an-element-of .} --> G(.) (a.s.) if and only if (1/log N)SIGMA(k less-than-or-equal-to N)(1/k)P(S(k)/a(k) is-an-element-of .) --> G(.). A functional version of this result also holds. For partial sums of ...
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作者：DYNKIN, EB
摘要：The subject of this article is a class of measure-valued Markov processes. A typical example is super-Brownian motion . The Laplacian DELTA plays a fundamental role in the theory of Brownian motion. For super-Brownian motion, an analogous role is played by the operator DELTAu - psi(u), where a nonlinear function psi describes the branching mechanism. The class of admissible functions psi includes the family psi(u) = u(alpha), 1 < alpha less-than-or-equal-to 2. Super-Brownian motion belongs to ...
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作者：SATO, KI
摘要：For any positive integer n, there exists a unimodal distribution mu such that mu * mu is n-modal. Furthermore, there is a unimodal distribution mu such that mu * mu has infinitely many modes. Lattice analogues of the results are also given.
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作者：BOIVIN, D
作者单位：University System of Ohio; Ohio State University
摘要：Assign to each edge e of the square lattice Z2 a random bond conductivity c(e). If c(e) are stationary, ergodic and such that 0 < a < c(e) < b < infinity for all edges e, then there is a central limit theorem for the corresponding reversible random walk on the lattice which holds for almost all environments.
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作者：GOUET, R
摘要：In a generalized two-color Polya urn scheme, allowing negative replacements, we use martingale techniques to obtain weak invariance principles for the urn process (W(n)), where W(n) is the number of white balls in the urn at stage n. The normalizing constants and the limiting Gaussian process are shown to depend on the ratio of the eigenvalues of the replacement matrix.
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作者：DEVALK, V
摘要：A representation of one-dependent processes is given in terms of Hilbert spaces, vectors and bounded linear operators on Hilbert spaces. This generalizes a construction of one-dependent processes that are not two-block-factors. We show that all one-dependent processes admit a representation. We prove that if there is in the Hilbert space a closed convex cone that is invariant under certain operators and that is spanned by a finite number of linearly independent vectors, then the corresponding ...
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作者：ENCHEV, O
摘要：The nonlinear filtering problem is studied for models where the samples of the signal and the noise are elements of some general abstract Wiener space. The signal is allowed to depend on the noise and the optimal filter is expressed as an explicit functional of the observed sample (trajectory). It is shown that this functional satisfies the Zakai equation. As a n technical tool, a class of shift transformations on the Wiener space is studied and an analog of Cameron-Martin-Girsanov's theorem i...
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作者：BURTON, R; PEMANTLE, R
作者单位：University of Wisconsin System; University of Wisconsin Madison
摘要：Let G be a finite graph or an infinite graph on which Z(d) acts with finite fundamental domain. If G is finite, let T be a random spanning tree chosen uniformly from all spanning trees of G; if G is infinite, methods from Pemantle show that this still makes sense, producing a random essential spanning forest of G. A method for calculating local characteristics (i.e., finite-dimensional marginals) of T from the transfer-impedance matrix is presented. This differs from the classical matrix-tree ...
