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作者：Broman, EI
作者单位：Chalmers University of Technology
摘要：Given a trigonometric polynomial f : [0, 1] -> [0, 1] of degree m, one can define a corresponding stationary process {X-i}(i is an element of Z) via determinants of the Toeplitz matrix for f. We show that for m = 1 this process, which is trivially one-dependent, is a two-block-factor.
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作者：Adler, M; van Moerbeke, P
作者单位：Brandeis University
摘要：In a celebrated paper, Dyson shows that the spectrum of an n x n random Hermitian matrix, diffusing according to an Ornstein-Uhlenbeck process, evolves as n noncolliding Brownian motions held together by a drift term. The universal edge and bulk scalings for Hermitian random matrices, applied to the Dyson process, lead to the Airy and Sine processes. In particular, the Airy process is a continuous stationary process, describing the motion of the outermost particle of the Dyson Brownian motion,...
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作者：Taylor, J; Takemura, A; Adler, RJ
作者单位：Stanford University; University of Tokyo; Technion Israel Institute of Technology
摘要：We study the accuracy of the expected Euler characteristic approximation to the distribution of the maximum of a smooth, centered, unit variance Gaussian process f. Using a point process representation of the error, valid for arbitrary smooth processes, we show that the error is in general exponentially smaller than any of the terms in the approximation. We also give a lower bound on this exponential rate of decay in terms of the maximal variance of a family of Gaussian processes f(x), derived...
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作者：Pardoux, E; Veretennikov, AY
作者单位：Aix-Marseille Universite; University of Leeds; Kharkevich Institute for Information Transmission Problems of the RAS
摘要：We study the Poisson equation Lu + f = 0 in R-d, where L is the infinitesimal generator of a diffusion process. In this paper, we allow the second-order part of the generator L to be degenerate, provided a local condition of Doeblin type is satisfied, so that, if we also assume a condition on the drift which implies recurrence, the diffusion process is ergodic. The equation is understood in a weak sense. Our results are then applied to diffusion approximation.
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作者：Balan, RM
作者单位：University of Ottawa
摘要：In this paper we generalize Yu's [Ann. Probab. 24 (1996) 2079-2097] strong invariance principle for associated sequences to the multi-parameter case, under the assumption that the covariance coefficient u(n) decays exponentially as n -> infinity. The main tools that we use are the following: the Berkes and Morrow [Z. Wahrsch. Verw. Gebiete 57 (1981) 15-37] multiparameter blocking technique, the Csorgo and Revesz [Z. Wahrsch. Verw.. Gebiete 31 (1975) 255-260] quantile transform method and the B...
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作者：Bramson, M; Liggett, TM
作者单位：University of Minnesota System; University of Minnesota Twin Cities; University of California System; University of California Los Angeles
摘要：There has been significant progress recently in our understanding of the stationary measures of the exclusion process on Z. The corresponding situation in higher dimensions remains largely a mystery. In this paper we give necessary and sufficient conditions for a product measure to be stationary for the exclusion process on an arbitrary set, and apply this result to find examples on Z(d) and on homogeneous trees in which product measures are stationary even when they are neither homogeneous no...
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作者：Dzhaparidze, K; van Zanten, H
作者单位：Vrije Universiteit Amsterdam
摘要：In this paper we develop the spectral theory of the fractional Brownian motion (fBm) using the ideas of Krein's work on continuous analogous of orthogonal polynomials on the unit circle. We exhibit the functions which are orthogonal with respect to the spectral measure of the fBm and obtain an explicit reproducing kernel in the frequency domain. We use these results to derive an extension of the classical Paley-Wiener expansion of the ordinary Brownian motion to the fractional case.
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作者：Baik, J; Ben Arous, G; Péché, S
作者单位：University of Michigan System; University of Michigan; Swiss Federal Institutes of Technology Domain; Ecole Polytechnique Federale de Lausanne
摘要：We compute the limiting distributions of the largest eigenvalue of a complex Gaussian sample covariance matrix when both the number of samples and the number of variables in each sample become large. When all but finitely many, say r, eigenvalues of the covariance matrix are the same, the dependence of the limiting distribution of the largest eigenvalue of the sample covariance matrix on those distinguished r eigenvalues of the covariance matrix is completely characterized in terms of an infin...
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作者：Penrose, MD
作者单位：University of Bath
摘要：Suppose X = (X-x, x in Z(d)) is a family of i.i.d. variables in some measurable space, B-0 is a bounded set in R-d, and for t > 1, H-t is a measure on t B-0 determined by the restriction of X to lattice sites in or adjacent to t B-0. We prove convergence to a white noise process for the random measure on B0 given by t(-d/2)(H-t(tA) - EHt (tA)) for subsets A of B-0, as t becomes large, subject to H satisfying a stabilization condition (whereby the effect of changing X at a single site x is loca...
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作者：Siegmund, D; Yakir, B
作者单位：Stanford University; Hebrew University of Jerusalem
摘要：An urn model of Diaconis and some generalizations are discussed. A convergence theorem is proved that implies for Diaconis' model that the empirical distribution of balls in the urn converges with probability one to the uniform distribution.
