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作者：Asmussen, S
作者单位：Lund University
摘要：Consider a reflected random walk W(n+1) = (W(n) +X(n))(+), where X(o), X(1),... are i.i.d. with negative mean and subexponential with common distribution F. It is shown that the probability that the maximum within a regenerative cycle with mean mu exceeds x is approximately mu (F) over bar(x) as x --> infinity, and thereby that max (W(o),..., W(n)) has the same asymptotics as max(X(o),...,X(n)) as n --> infinity. In particular, the extremal index is shown to be theta = 0, and the point process...
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作者：Cot, C; Catoni, O
作者单位：Centre National de la Recherche Scientifique (CNRS); Centre National de la Recherche Scientifique (CNRS); Universite Paris Saclay
摘要：We investigate how to tune a generalized simulated annealing algorithm with piecewise constant cooling schedule to get an optical convergence exponent. The optimal convergence exponent of generalized simulated annealing algorithms has been computed by Catoni and Trouve. It is reached only with triangular sequences of temperatures, meaning that different finite sequences are used, depending on the time resource available for computations (expressed by an overall number of iterations). We show f...
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作者：Tierney, L
作者单位：University of Minnesota System; University of Minnesota Twin Cities
摘要：The Metropolis-Hastings algorithm is a method of constructing a reversible Markov transition kernel with a specified invariant distribution. This note describes necessary and sufficient conditions on the candidate generation kernel and the acceptance probability function for the resulting transition kernel and invariant distribution to satisfy the detailed balance conditions. A simple general formulation is used that covers a range of special cases treated separately in the literature. In addi...
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作者：Alanyali, M; Hajek, B
作者单位：Alcatel-Lucent; Lucent Technologies; AT&T; University of Illinois System; University of Illinois Urbana-Champaign; University of Illinois System; University of Illinois Urbana-Champaign
摘要：This paper establishes a process-level large deviations principle for Markov processes in the Euclidean space with a discontinuity in the transition mechanism along a hyperplane. The transition mechanism of the process is assumed to be continuous on one closed half-space and also continuous on the complementary open half-space. Similar results were recently obtained for discrete time processes by Dupuis and Ellis and by Nagot. Our proof relies on the work of Blinovskii and Dobrushin, which in ...
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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...
