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作者：Betz, Volker; Ueltschi, Daniel; Velenik, Yvan
作者单位：University of Warwick; University of Geneva
摘要：We study the distribution of cycle lengths in models of nonuniform random permutations with cycle weights. We identify several regimes. Depending on the weights, the length of typical cycles grows like the total number n of elements, or a fraction of n or a logarithmic power of n.
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作者：Bai, Z. D.; Liu, H. X.; Wong, W. K.
作者单位：Northeast Normal University - China; Northeast Normal University - China; National University of Singapore; Hong Kong Baptist University
摘要：Let S(n) = 1/nX(n)X*(n) where X(n) = {X(ij)} is a p x n matrix with i.i.d. complex standardized entries having finite fourth moments. Let Y(n)(t(1), t(2), sigma) = root p(x(n)(t(1))*(S(n) + sigma I)(-1)x(n)(t(2)) - x(n)(t(1))*x(n)(t(2)) m(n)(sigma)) in which sigma > 0 and m(n)(sigma) = integral dF(yn)(x)/x+sigma where F(yn)(x) is the Marcenko-Pastur law with parameter y(n) = p/n; which converges to a positive constant as n -> infinity, and x(n)(t(1)) and x(n)(t(2)) are unit vectors in C(p), ha...
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作者：Kuna, Tobias; Lebowitz, Joel L.; Speer, Eugene R.
作者单位：University of Reading; Rutgers University System; Rutgers University New Brunswick
摘要：We give necessary and sufficient conditions for a pair of (generalized) functions rho(1)(r(1)) and rho(2) (r(1), r(2)), r(i) is an element of X, to be the density and pair correlations of some point process in a topological space X, for example, R(d), Z(d) or a subset of these. This is an infinite-dimensional version of the classical truncated moment problem. Standard techniques apply in the case in which there can be only a bounded number of points in any compact subset of X. Without this res...
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作者：Jacka, Saul; Warren, Jon; Windridge, Peter
作者单位：University of Warwick
摘要：Suppose we have three independent copies of a regular diffusion on [0, 1] with absorbing boundaries. Of these diffusions, either at least two are absorbed at the upper boundary or at least two at the lower boundary. In this way, they determine a majority decision between 0 and 1. We show that the strategy that always runs the diffusion whose value is currently between the other two reveals the majority decision whilst minimizing the total time spent running the processes.
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作者：Kruk, Lukasz; Lehoczky, John; Ramanan, Kavita; Shreve, Steven
作者单位：Maria Curie-Sklodowska University; Polish Academy of Sciences; Institute of Mathematics of the Polish Academy of Sciences; Brown University; Carnegie Mellon University; Carnegie Mellon University
摘要：This paper presents a heavy-traffic analysis of the behavior of a single-server queue under an Earliest-Deadline-First (EDF) scheduling policy in which customers have deadlines and are served only until their deadlines elapse. The performance of the system is measured by the fraction of reneged work (the residual work lost due to elapsed deadlines) which is shown to be minimized by the EDF policy. The evolution of the lead time distribution of customers in queue is described by a measure-value...
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作者：Belomestny, Denis
作者单位：Leibniz Association; Weierstrass Institute for Applied Analysis & Stochastics
摘要：In this paper, we study simulation-based optimization algorithms for solving discrete time optimal stopping problems. Using large deviation theory for the increments of empirical processes, we derive optimal convergence rates for the value function estimate and show that they cannot be improved in general. The rates derived provide a guide to the choice of the number of simulated paths needed in optimization step, which is crucial for the good performance of any simulation-based optimization a...
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作者：Marty, Renaud; Solna, Knut
作者单位：University of California System; University of California Irvine; Universite de Lorraine
摘要：We consider waves propagating in a randomly layered medium with long-range correlations. An example of such a medium is studied in [19] and leads, in particular, to an asymptotic travel time described in terms of a fractional Brownian motion. Here we study the asymptotic transmitted pulse under very general assumptions on the long-range correlations. In the framework that we introduce in this paper, we prove in particular that the asymptotic time-shift can be described in terms of non-Gaussian...
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作者：Constantin, Peter; Iyer, Gautam
作者单位：University of Chicago; Carnegie Mellon University
摘要：In this paper we derive a probabilistic representation of the deterministic 3-dimensional Navier-Stokes equations in the presence of spatial boundaries. The formulation in the absence of spatial boundaries was done by the authors in [Comm. Pure Appl. Math. 61 (2008) 330-345]. While the formulation in the presence of boundaries is similar in spirit, the proof is somewhat different. One aspect highlighted by the formulation in the presence of boundaries is the nonlocal, implicit influence of the...
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作者：Chatterjee, Sourav; Shao, Qi-Man
作者单位：New York University; Hong Kong University of Science & Technology
摘要：where g(W) is a dominated term and r(W) is negligible. Let G(t) = f(0)(t)g(s)ds and define p(t) = c1e(-c0G(t)), where c(0) is a properly chosen constant and c(1) = 1/integral(infinity)(-infinity) e(-c0G(t)) dt. Let Y be a random variable with the probability density function p. It is proved that W converges to Y in distribution when the conditional second moment of (W - W') given W satisfies a law of large numbers. A Berry-Esseen type bound is also given. We use this technique to obtain a Berr...
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作者：Zhang, Jiheng; Dai, J. G.; Zwart, Bert
作者单位：Hong Kong University of Science & Technology; University System of Georgia; Georgia Institute of Technology; Centrum Wiskunde & Informatica (CWI)
摘要：We consider a processor sharing queue where the number of jobs served at any time is limited to K, with the excess jobs waiting in a buffer. We use random counting measures on the positive axis to model this system. The limit of this measure-valued process is obtained under diffusion scaling and heavy traffic conditions. As a consequence, the limit of the system size process is proved to be a piece-wise reflected Brownian motion.
