-
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.
-
作者：ROCHA, AL
摘要：The infinite secretary problem, in which an infinite number of rankable items arrive at times which are i.i.d., uniform on (0, 1), is modified to allow for a fixed period of recall of length alpha, 0 less-than-or-equal-to alpha less-than-or-equal-to 1. The goal is to find the maximum probability of best choice, v = v(alpha), as well as an optimal stopping time tau* = tau*(alpha). A differential-delay equation is derived, the solution of which yields v(alpha) and tau*(a), the latter given in te...
-
作者：SCHNEEMEIER, W
摘要：Empirical processes of U-statistic structure were introduced by Serfling and studied in detail by Silverman, who proved weak convergence of weighted versions in the i.i.d. case. Our main theorem shows that this result can be generalized in two directions: First, the i.i.d. assumption can be omitted, and second, our proof holds for a richer class of weight functions. In addition, we obtain almost sure convergence of weighted U-processes in the i.i.d. case which improves the results of Helmers, ...
-
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 ...
-
作者：DIACONIS, P; SALOFFCOSTE, L
作者单位：Centre National de la Recherche Scientifique (CNRS); Sorbonne Universite
摘要：We develop techniques for bounding the rate of convergence of a symmetric random walk on a finite group to the uniform distribution. The techniques gives bounds on the second largest (and other) eigenvalues in terms of the eigenvalues of a comparison chain with known eigenvalues. The techniques yield sharp rates for a host of previously intractable problems on the symmetric group.
-
作者：GEORGII, HO
摘要：We present a new approach to the principle of large deviations for the empirical field of a Gibbsian random field on the integer lattice Z(d). This approach has two main features. First, we can replace the traditional weak topology by the finer topology of convergence of cylinder probabilities, and thus obtain estimates which are finer and more widely applicable. Second, we obtain as an immediate consequence a limit theorem for conditional distributions under conditions on the empirical field,...
-
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...
-
作者：TANEMURA, H
摘要：A random walk with obstacles in R(d), d greater-than-or-equal-to 2, is considered. A probability measure is put on a space of obstacles, giving a random walk with random obstacles. A central limit theorem is then proven for this process when the obstacles are distributed by a Gibbs state with sufficiently low activity. The same problem is treated for a tagged particle of an infinite hard core particle system.
-
作者：HAIMAN, G; PURI, ML
作者单位：Indiana University System; Indiana University Bloomington
摘要：It is shown that in the case of stationary Gaussian processes, the Jth (J greater-than-or-equal-to 1) record times {T(n), n greater-than-or-equal-to 1} and the corresponding J-upper order statistics {X(Tn-J+1,Tn),...,X(Tn,Tn)} can almost surely be identified via a translation of the time index n to the corresponding elements defined on a sequence of independent and identically distributed random variables. A construction method for approximating sequences of record times and the corresponding ...
-
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 ...
