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作者：Klass, MJ; Nowicki, K
作者单位：University of California System; University of California Berkeley; University of California System; University of California Berkeley; Lund University
摘要：Let X-1, Y-1, Y-2,..., X-n, Y-n be independent nonnegative rv's and let {b(ij)}(1 less than or equal to i, j less than or equal to n) be an array of nonnegative constants. We present a method of obtaining the order of magnitude of E Phi (Sigma(1 less than or equal to i, j less than or equal to n) b(ij) X-i Y-j), for any such {X-i}, {Y-i} and {b(ij)} and any nondecreasing function Phi on [0, infinity) with Phi(0) = 0 and satisfying a Delta(2) growth condition Furthermore, this technique is exte...
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作者：Alexander, KS
作者单位：University of Southern California
摘要：For a nonnegative subadditive function h on Z(d), with limiting approximation g(x) = lim(n) h(nx)/n, it is of interest to obtain bounds on the discrepancy between g(x) and h(x), typically of order \x\(nu) with nu < 1. For certain subadditive h(x), particularly those which are expectations associated with optimal random paths from 0 to x, in a somewhat standardized way a more natural and seemingly weaker property can be established: every x is in a bounded multiple of the convex hull of the set...
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作者：Hennion, H
作者单位：Universite de Rennes
摘要：Let S be the set of q x q matrices with positive entries, such that each column and each row contains a strictly positive element, and denote by S degrees the subset of these matrices, all entries of which are strictly positive. Consider a random ergodic sequence (X-n)(n greater than or equal to 1) in S. The aim of this paper is to describe the asymptotic behavior of the random products X-(n) = X-n... X-1, n greater than or equal to 1, under the main hypothesis P(U)(n greater than or equal to ...
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作者：Hambly, BM
作者单位：University of Edinburgh
摘要：We introduce a random recursive fractal based on the Sierpinski gasket and construct a diffusion upon the fractal via a Dirichlet form. This form and its symmetrizing measure are determined by the electrical resistance of the fractal. The effective resistance provides a metric with which to discuss the properties of the fractal and the diffusion. The main result is to obtain uniform upper and lower bounds for the transition density of the Brownian motion on the fractal in terms of this metric....
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作者：Dynkin, EB; Kuznetsov, SE
作者单位：Russian Academy of Sciences; Central Economics & Mathematics Institute RAS
摘要：We investigate natural linear additive (NLA) functionals of a general critical (xi, K, psi)-superprocess X. We prove that all of them have only fixed discontinuities. All homogeneous NLA functionals of time-homogeneous superprocesses are continuous (this was known before only in the case of quadratic branching). We introduce an operator epsilon(u) defined in terms of (xi, K, psi) and we prove that the potential h and the log-potential u of a NLA functional A are connected by the equation u + e...
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作者：Bunge, J
作者单位：Cornell University
摘要：A random variable X is C-decomposable if X = (D) cX + Y-c for all c in C, where Y-c is a random variable independent of X and C is a closed multiplicative subsemigroup of [0, 1]. X is self-decomposable if C = [0, 1]. Extending an idea of Urbanik in the self-decomposable case, we define a decreasing sequence of subclasses of the class of C-decomposable laws, for any C. We give a structural representation for laws in these classes, and we show that laws in the limiting subclass are infinitely di...
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作者：Grama, IG
作者单位：Academy of Sciences of Moldova
摘要：Let X-n = (X-t(n), F-t(n))(0 less than or equal to t less than or equal to 1) be square integrable martingales with the quadratic characteristics [X-n], n = 1, 2, .... We prove that the large deviations relation P(X-1(n) greater than or equal to r)/(1 - Phi(r)) --> 1 holds true for r growing to infinity with some rate depending on L-2 delta(n) = E Sigma(0 less than or equal to t less than or equal to 1) \Delta X-t(n)\(2+2 delta) and N-2 delta(n) = E\[X-n](1) - 1\(1+delta), where delta > 0 and ...
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作者：De La Pena, VH; Lai, TL
作者单位：Columbia University; Stanford University
摘要：In this paper we provide sharp bounds on the L-p-norms of randomly stopped U-statistics. These bounds consist mainly of decoupling inequalities designed to reduce the level of dependence between the U-statistics and the stopping time involved. we apply our results to obtain Wald's equation for U-statistics, moment convergence theorems and asymptotic expansions for the moments of randomly stopped U-statistics. The proofs are based an decoupling inequalities, symmetrization techniques, the use o...
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作者：Fleming, WH; Sheu, SJ
作者单位：Brown University; Academia Sinica - Taiwan
摘要：The asymptotic behaviors of the principal eigenvalue and the corresponding normalized eigenfunction of the operator G(epsilon) f = (epsilon/2)Delta f + g del f + (l/epsilon)f for Small epsilon are studied. Under some conditions, the first order expansions for them are obtained. Two applications to risk-sensitive control problems are also mentioned.
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作者：Newman, CM; Wu, CC
作者单位：New York University; Pennsylvania Commonwealth System of Higher Education (PCSHE); Pennsylvania State University
摘要：We consider inhomogeneous nearest neighbor Bernoulli bond percolation on Z(d) where the bonds in a fixed s-dimensional hyperplane (1 less than or equal to s less than or equal to d - 1) have density p(1) and all other bonds have fixed density, p(c)(Z(d)), the homogeneous percolation critical value. For s greater than or equal to 2, it is natural to conjecture that there is a new critical value, p(c)(s)(Z(d)), for p(1), strictly between p(c)(Z(d)) and p(c)(Z(s)); we prove this for large d and 2...
