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作者：Xia, Aihua
作者单位：University of New South Wales Sydney
摘要：This paper investigates an alternative way of using the Stein-Chen method in Poisson approximations. There are three principal bounds stated in terms of reduced Palm probabilities for general point processes. The first two are for the accuracy of Poisson random variable approximation to the distribution of the number of points in a point process with respect to the total variation metric and the Wasserstein metric, and the third is for bounding the errors of Poisson process approximation to th...
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作者：Seppalainen, Timo
作者单位：Iowa State University
摘要：We derive a law of large numbers for a tagged particle in the one-dimensional totally asymmetric simple exclusion process under a scaling different from the usual Euler scaling. By interpreting the particles as the servers of a series of queues we use this result to verify an open conjecture about the scaling behavior of the departure times from a long series of queues.
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作者：Anderson, Clive W.; Coles, Stuart G.; Husler, Jurg
作者单位：University of Sheffield; Lancaster University; University of Bern
摘要：It is known that maxima of independent Poisson variables cannot be normalized to converge to a nondegenerate limit distribution. On the other hand, the Normal distribution approximates the Poisson distribution for large values of the Poisson mean, and maxima of random samples of Normal variables may be linearly scaled to converge to a classical extreme value distribution. We here explore the boundary between these two kinds of behavior. Motivation comes from the wish to construct models for th...
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作者：Marquez, David
作者单位：University of Central Venezuela; Universite Gustave-Eiffel
摘要：We consider the annealing diffusion process and investigate convergence rates. Namely, for the diffusion dX(t) = -del V(X-f)dt + sigma(t)dB(f), where (B-f)(l) <= 0 is the sigma(t) dimensional Brownian motion and cr(t) decreases to zero, we prove a large deviation principle for (V(X-t)) and weak convergence of(sigma(-2)(t)(V(X-f) - inf V)).
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作者：Seppalainen, Timo
作者单位：Iowa State University
摘要：In 1977 Vershik and Kerov deduced the asymptotic normalized length of the longest increasing sequence among independent points uniformly distributed on the unit square. We solve the analogous problem for points on the planar square lattice that are present independently of each other.
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作者：Stadje, Wolfgang
作者单位：University Osnabruck
摘要：This paper is concerned with Markov chain models for flows of a finite population among a set of groups, where the individuals base their decisions on which group to go next partially on the current frequency distribution (profile). For a certain class of these models, the transition matrix of the profile process is analyzed algebraically, leading to surprisingly simple asymptotic results. Furthermore, in a model with after effects, the absorption probabilities are derived.
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作者：Bean, N. G.; Gibbens, R. J.; Zachary, S.
作者单位：University of Adelaide; University of Cambridge; Heriot Watt University
摘要：We study the behavior of large loss networks in which the offered traffic is subject to acceptance controls. Hunt and Kurtz proved a functional law of large numbers for the dynamics of such networks, as capacity and offered traffic are allowed to increase in proportion. However, limiting dynamics were not in general uniquely identified. We establish further results identifying these dynamics under given conditions. We also investigate the existence of fixed points for these dynamics and relate...
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作者：Hunt, P. J.; Laws, C. N.
作者单位：University of Oxford
摘要：Trunk reservation is a simple, robust and extremely effective mechanism for controlling loss systems which allows priority to be given to chosen traffic streams. We consider the control of a single resource under a limiting regime in which capacity and arrival rates increase together. We obtain trunk reservation control policies which are asymptotically optimal when calls have differing capacity requirements, holding times, arrival rates and reward rates. The priority levels associated with th...
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作者：Ossiander, Mina; Waymire, Ed; Zhang, Qing
作者单位：Oregon State University
摘要：Consider a rooted labelled tree graph tau(n) having a total of n vertices. The width function counts the number of vertices as a function of the distance to the root phi. In this paper we compute large n asymptotic behavior of the width functions for two classes of tree graphs (both random and deterministic) of the following types: (i) Galton-Watson random trees tn conditioned on total progeny and (ii) a class of deterministic self-similar trees which include an expected Galton-Watson tree in ...
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作者：Goldstein, Larry; Reinert, Gesine
作者单位：University of Southern California; University of Southern California
摘要：Let W be a random variable with mean zero and variance sigma(2). The distribution of a variate W*, satisfying EWf(W). = sigma 2Ef' (W*). for smooth functions f, exists uniquely and defines the zero bias transformation on the distribution of W. The zero bias transformation shares many interesting properties with the well-known size bias transformation for nonnegative variables, but is applied to variables taking on both positive and negative values. The transformation can also be defined on mor...
