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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：Berger, Erich
作者单位：University of Gottingen
摘要：In this paper we consider a class of stochastic approximation procedures that arises in linear filtering and regression theory. Our main result asserts that the stochastic approximation process satisfies an almost sure invariance principle (with a certain rate of convergence) if the partial sums of the errors do.
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作者：Roberts, G. O.; Gelman, A.; Gilks, W. R.
作者单位：University of Cambridge; Columbia University; University of Cambridge; MRC Biostatistics Unit
摘要：This paper considers the problem of scaling the proposal distribution of a multidimensional random walk Metropolis algorithm in order to maximize the efficiency of the algorithm. The main result is a weak convergence result as the dimension of a sequence of target densities, n, converges to infinity. When the proposal variance is appropriately scaled according to n, the sequence of stochastic processes formed by the first component of each Markov chain converges to the appropriate limiting Lan...
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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：Lange, Kenneth; Zhao, Hongyu; Speed, Terence P.
作者单位：University of Michigan System; University of Michigan; Yale University; University of California System; University of California Berkeley
摘要：The Poisson-skip model introduced in this paper generalizes the chi-quare model of crossover interference. Both models are constructed from the random points of a Poisson process occurring along a meiotic bundle of four chromatids. The points of the Poisson process are divided into X points and o points, with X points corresponding to crossovers. In the chi-square model, a fixed number of o points intervene between every adjacent pair of X points; in the Poisson-skip model, a random number of ...
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作者：Boehm, W.; Mohanty, S. G.
作者单位：McMaster University
摘要：In this paper we present some interesting results which follow from the celebrated determinant formulas for noncoincidence probabilities of Markov processes discovered by Karlin and McGregor. The first theorem is a determinant formula for the probability that a Markov jump process will avoid a certain finite set of points. From this theorem a simple solution of the moving boundary problem for certain types of Markov processes can be obtained. The other theorems deal with noncoincidence probabi...
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作者：Bertoin, Jean
作者单位：Sorbonne Universite
摘要：Consider a completely asymmetric Levy process which has absolutely continuous transition probabilities. We determine the exponential decay parameter rho and the quasistationary distribution for the transition probabilities of the evy process killed as it exits from a finite interval, prove that the killed process is rho-positive and specify the rho-invariant function and measure.
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作者：O'Neill, Philip
作者单位：University of Bradford
摘要：This paper is concerned with a model for the spread of an epidemic in a closed, homogeneously mixed population in which new infections occur at rate beta(z)xy/(x+y), where x, y and z denote, respectively, the numbers of susceptible, infective and removed individuals. Thus the infection mechanism depends upon the number of removals to date, reflecting behavior change in response to the progress of the epidemic. For a deterministic version of the model, a recurrent solution is obtained when beta...
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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：Chassaing, Philippe
作者单位：Universite de Lorraine
摘要：We are given a set of n elements, some of them red, the others blue, but their colors are hidden. We are to determine the composition of this set, or to determine an element of the majority color, by making pairwise comparisons of elements from which we obtain the information the colors of these two elements are the same,'' or they are different.'' Let tau(n), respectively, mu(n), be the optimal average number of comparisons needed to solve these two problems. We give an explicit expression of...
