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作者：Dembo, Amir; Karlin, Samuel; Zeitouni, Ofer
作者单位：Stanford University; Stanford University; Technion Israel Institute of Technology
摘要：Three results on hitting a rare set by the increments of an R-d-valued random process with stationary independent increments are presented: the first time that it occurs, the duration of such a segment and the typical trajectory during the segment.
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作者：Bramson, Maury
作者单位：University of Wisconsin System; University of Wisconsin Madison
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作者：Ferrari, P. A.; Fontes, L. R. G.
作者单位：Universidade de Sao Paulo
摘要：We study a system of infinitely many queues with Poisson arrivals and exponential service times. Let the net output process be the difference between the departure process and the arrival process. We impose certain ergodicity conditions on the underlying Markov chain governing the customer path. These conditions imply the existence of an invariant measure under which the average net output process is positive and proportional to the time. Starting the system with that measure, we prove that th...
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作者：Malyshev, Vadim; Robert, Philippe
作者单位：Lomonosov Moscow State University; Inria
摘要：In this paper we analyze the following loss network: When a customer arrives at a node of the network, it is served by this node if the node is not occupied; otherwise it is transmitted to some empty node where it will be served at a different rate. For the simplest systems of this type with a very large number of nodes and with global sharing, we show the existence of second order phase transitions and present explicit formulas for probability characteristics. For local sharing, we study the ...
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作者：Deuschel, Jean-Dominique; Mazza, Christian
作者单位：Swiss Federal Institutes of Technology Domain; ETH Zurich; University of Fribourg
摘要：We study the convergence of nonsymmetric annealing processes, extending the classical Dirichlet form approach to a broad class of Markov chains with exponentially vanishing transition functions. We show that both the true and symmetrized spectral gaps are logarithmically equivalent, and give robust estimates for the gap using geometric methods.
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作者：Massey, William A.; Whitt, Ward
作者单位：AT&T; Nokia Corporation; Nokia Bell Labs
摘要：A fundamental problem that led to the development of queueing theory is the probabilistic modelling of the number of busy lines in telephone trunk groups. Based on the behavior of real telephone systems, a natural model to use would be the M-t/G/s/0 queue, which has s servers, no extra waiting space and a nonhomogeneous Poisson arrival process (M-t). Unfortunately, so far queueing theory has provided an exact analysis for only the M/G/s/0 queue in steady state, which yields the Erlang blocking...
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作者：Quine, M. P.; Szczotka, W.
作者单位：University of Sydney
摘要：We define a stochastic process H = (X-n = 0, 1, 2, ...) in terms of cumulative sums of the sequence K-1, K-2, ... of integer-valued random variables in such a way that if the K-i, are independent, identically distributed and nonnegative, then H is a Bienayme Galton Watson branching process. By exploiting the fact that H is in a sense embedded in a random walk, we show that some standard branching process results hold in more general settings. We also prove a new type of limit result.
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作者：Berman, Simeon M.
作者单位：New York University
摘要：Let Z be a normal random vector in R-k and let 1 be the element of R-k with equal components 1. Let X be a random variable that is independent of Z and consider the sum Z + X 1. The latter has a normal distribution in Rk if and only if X has a normal distribution in R1. The first result of this paper is a formula for a uniform bound on the difference between the density function of Z + X1 and the density function in the case where X has a suitable normal distribution. This is applied to a prob...
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作者：Hsing, Tailen
作者单位：Texas A&M University System; Texas A&M University College Station
摘要：The asymptotic distribution of the area V-n outside the convex hull of n i.i.d. points uniformly distributed on the two-dimensional unit disk is studied. The asymptotic variance of V-n is found to be of the order n(-5/3), and the asymptotic distribution of V-n shown to be normal. The results are obtained by carefully analyzing the strength of dependence between sample points at different locations close to the boundary of the unit disk.
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作者：Keener, Robert W.
作者单位：University of Michigan System; University of Michigan
摘要：Let T = inf{n >= 1: S-n > 0} and H = S-T be ladder variables for a random walk {S-n}(n >= 1) with nonnegative drift. Integral formulas for generating functions and moments of T, H and related quantities are developed. These formulas are suitable for numerical quadrature and should be easier to implement than formulas based on Spitzer's identity when the distribution of S-n is complicated. The approach used makes key use of the Hilbert transform and the main regularity assumption is that some p...
