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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：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：Chiu, S. N.; Quine, M. P.
作者单位：Hong Kong Baptist University; University of Sydney
摘要：A Poisson point process Psi in d-dimensional Euclidean space and in time is used to generate a birth-growth model: seeds are born randomly at locations x(i) in R-d at times t(i) is an element of [0, infinity). Once a seed is born, it begins to create a cell by growing radially in all directions with speed nu > 0. Points of Psi contained in such cells are discarded, that is, thinned. We study the asymptotic distribution of the number of seeds in a region, as the volume of the region tends to in...
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作者：Bouton, Catherine; Pages, Gilles
作者单位：heSam Universite; Universite Pantheon-Sorbonne; Sorbonne Universite; Universite Paris-Est-Creteil-Val-de-Marne (UPEC)
摘要：The competitive learning vector quantization (CLVQ) algorithm with constant step epsilon > 0-also known as the Kohonen algorithm with 0 neighbors-is studied when the stimuli are i.i.d. vectors. Its first noticeable feature is that, unlike the one-dimensional case which has n! absorbing subsets, the CLVQ algorithm is irreducible on open sets whenever the stimuli distribution has a path-connected support with a nonempty interior. Then the Doeblin recurrence (or uniform ergodicity) of the algorit...
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作者：Jones, Owen Dafydd
作者单位：University of Sheffield
摘要：Using the ergodic theory of nonnegative matrices, conditions are obtained for the L-2 and almost sure convergence of a supercritical multitype branching process with varying environment, normed by its mean. We also give conditions for the extinction probability of the limit to equal that of the process. The theory developed allows for different types to grow at different rates, and an example of this is given, taken from the construction of a spatially inhomogeneous diffusion on the Sierpinski...
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作者：Bramson, Maury; Neuhauser, Claudia
作者单位：University of Wisconsin System; University of Wisconsin Madison; University of Minnesota System; University of Minnesota Twin Cities
摘要：We consider a two-dimensional catalytic surface reaction between X and Y-n with Y-n + nX -> nXY, where Y-n is a polymer consisting of n identical atoms, each denoted by Y, and X is a monomer. The reactants X and Y-n are present above the surface in a gaseous phase, and bond to the surface at certain rates. The resulting atoms X and Y on the surface react if they are sufficiently close to each other; the product XY then leaves the surface, A classical example is the oxidation of carbon monoxide...
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作者：Calvin, James M.
作者单位：New Jersey Institute of Technology
摘要：We describe a class of adaptive algorithms for approximating the global minimum of a continuous function on the unit interval. The limiting distribution of the error is derived under the assumption of Wiener measure on the objective functions. For any delta > 0, we construct an algorithm which has error converging to zero at rate n(-(1-delta)) in the number of function evaluations n. This convergence rate contrasts with the n(-1/2) rate of previously studied nonadaptive methods.
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作者：Hall, Peter; Raimondo, Marc
作者单位：Australian National University; Commonwealth Scientific & Industrial Research Organisation (CSIRO)
摘要：Throw a straight line at random into a plane, within which is inscribed a square grid. Color black each grid vertex that lies above the line, and white each vertex below it. Now remove the line, and attempt to reconstruct it from the pattern of vertex colors in an m x m section of the grid. We show that for all epsilon > 0, the line can be approximated to within order m(-1) (log m)(log log m)(1+epsilon), with probability 1, and that there is no deterministic subsequence along which the best ac...
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作者：Stefanov, V. T.; Pakes, A. G.
作者单位：University of Western Australia
摘要：A new and unified approach is presented for constructing joint generating functions for quantities of interest associated with pattern formation in binary sequences. The method is based on results on exponential families of Markov chains. The tools we use are not only new for this area; they seem to be the right approach for deriving general explicit distributional results.
