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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：Glasserman, Paul; Wang, Yashan
作者单位：Columbia University
摘要：A guiding principle in the efficient estimation of rare-event probabilities by Monte Carlo is that importance sampling based on the change of measure suggested by a large deviations analysis can reduce variance by many orders of magnitude. In a variety of settings, this approach has led to estimators that are optimal in an asymptotic sense. We give examples, however, in which importance sampling estimators based on a large deviations change of measure have provably poor performance. The estima...
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作者：Gravner, Janko; Griffeath, David
作者单位：University of California System; University of California Davis; University of Wisconsin System; University of Wisconsin Madison
摘要：A Poisson-Voronoi tessellation (PVT) is a tiling of the Euclidean plane in which centers of individual tiles constitute a Poisson field and each tile comprises the locations that are closest to a given center with respect to a prescribed norm. Many spatial systems in which rare, randomly distributed centers compete for space should be well approximated by a PVT. Examples that we can handle rigorously include multitype threshold vote automata, in which k different camps compete for voters stati...
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作者：Molchanov, S. A.; Surgailis, D.; Woyczynski, W. A.
作者单位：University of North Carolina; University of North Carolina Charlotte; Vilnius University; University System of Ohio; Case Western Reserve University; University System of Ohio; Case Western Reserve University
摘要：Burgers turbulence is an accepted formalism for the adhesion model of the large-scale distribution of matter in the universe. The paper uses variational methods to establish evolution of quasi-Voronoi (curved boundaries) tessellation structure of shock fronts for solutions of the inviscid nonhomogeneous Burgers equation in R-d in the presence of random forcing due to a degenerate potential. The mean rate of growth of the quasi-Voronoi cells is calculated and a scaled limit random tessellation ...
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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：Harrison, J. Michael; Van Mieghem, Jan A.
作者单位：Stanford University; Northwestern University
摘要：Brownian networks are a class of linear stochastic control systems that arise as heavy traffic approximations in queueing theory. Such Brownian system models have been used to approximate problems of dynamic routing, dynamic sequencing and dynamic input control for queueing networks. A number of specific examples have been analyzed in recent years, and in each case the Brownian network has been successfully reduced to an equivalent workload formulation of lower dimension. In this article we ex...
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作者：de Lima, A. C. Pedroso; Sen, Pranab K.
作者单位：Universidade de Sao Paulo; University of North Carolina; University of North Carolina Chapel Hill
摘要：A matrix-valued counting process that allows for modeling of multi-variate failure-time data is presented. the inclusion of covariates in a Cox-type regression model is considered, and asymptotic properties of the estimates of regression parameters appearing in the model are studied.
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作者：Levental, Shlomo; Skorohod, Anatolii V.
作者单位：Michigan State University
摘要：We study the continuous-time problem of hedging a generalized call option of the European and of the American type, in the presence of transaction costs. We show that if the price process of the relevant stock fluctuates with positive probability, then the only hedge that is possible for the American option is the trivial one. If the price of the stock, in addition to fluctuating with positive probability, is also stable with positive probability, then the same is true for the European option....
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作者：Rothmann, Mark D.; Russo, Ralph P.
作者单位：University System of Georgia; Georgia Institute of Technology; University of Iowa
摘要：Consider a system into which units having random magnitude enter at arbitrary times and remain active (present in the system) for random periods. Suppose units of high magnitude have stochastically greater lifetimes ffi tend to stay active for longer periods. than units of low magnitude. Of interest is the process {mu(t): t >= 0}, where mu(t) denotes the average magnitude of all units active at time t. We give conditions which guarantee the convergence of mu(t) and we determine the form of the...
