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作者：Doney, RA; Maller, RA
作者单位：University of Manchester; Australian National University; Australian National University
摘要：The natural analogue for a Levy process of Cramer's estimate for a reflected random walk is a statement about the exponential rate of decay of the tail of the characteristic measure of the height of an excursion above the minimum. We establish this estimate for any Levy process with finite negative mean which satisfies Cramer's condition, and give an explicit formula for the limiting constant. Just as in the random walk case, this leads to a Poisson limit theorem for the number of high excursi...
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作者：Goel, A; Rai, S; Krishnamachari, B
作者单位：Stanford University; Stanford University; Stanford University
摘要：Random geometric graphs result from taking n uniformly distributed points in the unit cube, [0, 1](d), and connecting two points if their Euclidean distance is at most r, for some prescribed r. We show that monotone properties for this class of graphs have sharp thresholds by reducing the problem to bounding the bottleneck matching oil two sets of n points distributed uniformly in [0, 1](d). We present upper bounds on the threshold width, and show that our bound is sharp for d = 1 and at most ...
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作者：Kebaier, A
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Paris-Est-Creteil-Val-de-Marne (UPEC); Universite Gustave-Eiffel
摘要：We study the approximation of Ef(X-T) by a Monte Carlo algorithm, where X is the solution of a stochastic differential equation and f is a given function. We introduce a new variance reduction method, which can be viewed as a statistical analogue of Romberg extrapolation method. Namely, we use two Euler schemes with steps delta and delta(beta), 0 < beta < 1. This leads to an algorithm which, for a given level of the statistical error, has a complexity significantly lower than the complexity of...
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作者：Foss, S; Palmowski, Z; Zachary, S
作者单位：Heriot Watt University; University of Wroclaw; Utrecht University
摘要：We study the asymptotic probability that a random walk with heavy-tailed increments crosses a high boundary on a random time interval. We use new techniques to extend results of Asmussen [Ann. Appl. Probab. 8 (1998) 354-374] to completely general stopping times, uniformity of convergence over all stopping times and a wide class of nonlinear boundaries. We also give some examples and counterexamples.
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作者：Christophi, CA; Mahmoud, HM
作者单位：George Washington University
摘要：We investigate A, the distance between randomly selected pairs of nodes among n keys in a random trie, which is a kind of digital tree. Analytical techniques, such as the Mellin transform and an excursion between poissonization and depoissonization, capture small fluctuations in the mean and variance of these random distances. The mean increases logarithmically in the number of keys, but curiously enough the variance remains O (1), as n -> infinity. It is demonstrated that the centered random ...
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作者：Sagitov, S; Jagers, P
作者单位：Chalmers University of Technology
摘要：We establish convergence to the Kingman coalescent for a class of age-structured population models with time-constant population size. Time is discrete with unit called a year. Offspring numbers in a year may depend on mother's age.
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作者：Arratia, R; Liggett, TM
作者单位：University of Southern California; University of California System; University of California Los Angeles
摘要：Given i.i.d. positive integer valued random variables D-1,..., D-n, one can ask whether there is a simple graph on n vertices so that the degrees of the vertices are D-1,..., D-n. We give sufficient conditions on the distribution of D-i for the probability that this be the case to be asymptotically 0, 2 or strictly between 0 and 2. These conditions roughly correspond to whether the limit of nP(D-i greater than or equal to n) is infinite, zero or strictly positive and finite. This paper is moti...
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作者：Luczak, MJ; Norris, J
作者单位：University of London; London School Economics & Political Science; University of Cambridge
摘要：We prove three strong approximation theorems for the supermarket or join the shortest queue model-a law of large numbers, a jump process approximation and a central limit theorem. The estimates are carried through rather explicitly, and rely in part on couplings. This allows us to approximate each of the infinitely many components of the process in its own scale and to exhibit a cut-off in the set of active components which grows slowly with the number of servers.
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作者：Garet, O; Marchand, R
作者单位：Universite de Orleans; Universite de Lorraine
摘要：We study the problem of coexistence in a two-type competition model governed by first-passage percolation on Z(d) or on the infinite cluster in Bernoulli percolation. We prove for a large class of ergodic stationary passage times that for distinct points x, y is an element of Z(d), there is a strictly positive probability that {z is an element of Z(d); d(y, z) < d(x, z)} and {z is an element of Z(d); d(y, z) > d(x, z)} are both infinite sets. We also show that there is a strictly positive prob...
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作者：Banner, AD; Fernholz, R; Karatzas, I
作者单位：Columbia University
摘要：Atlas-type models are constant-parameter models of uncorrelated stocks for equity markets with a stable capital distribution, in which the growth rates and variances depend on rank. The simplest such model assigns the same, constant variance to all stocks; zero rate of growth to all stocks but the smallest-, and positive growth rate to the smallest, the Atlas stock. In this paper we study the basic properties of this class of models, as well as the behavior of various portfolios in their midst...
