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作者：Barsky, David J.; Gandolfi, Alberto
作者单位：California State University System; California State University San Marcos; University of Rome Tor Vergata
摘要：In this paper we present an asymptotic estimator, obtained by observing a noisy image, for the parameters of both a stationary Markov random field and an independent Bernoulli noise. We first estimate the parameter of the noise by solving a polynomial equation of moderate degree (about 6-7 in the one-dimensional Ising model and about 10-15 in the two-dimensional Ising model, for instance) and then apply the maximum pseudo-likelihood method after removing the noise. Our method requires no extra...
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作者：Biggins, J. D.
作者单位：University of Sheffield
摘要：A general (Crump-Mode-Jagers) spatial branching process is considered. The asymptotic behavior of the numbers present at time t in sets of the form [ta, infinity) is obtained. As a consequence it is shown that if B-t is the position of the rightmost person at time t, B-t/t converges to a constant, which can be obtained from the individual reproduction law, almost surely on the survival set of the process. This generalizes the known discrete-time results.
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作者：Kallianpur, G.; Xiong, J.
作者单位：University of North Carolina; University of North Carolina Chapel Hill; University of Tennessee System; University of Tennessee Knoxville
摘要：Under suitable conditions, it is proved that limits of sequences of nuclear space-valued solutions of stochastic differential equations driven by Poisson random measures are characterized by diffusion equations. The results are applied to models of environmental pollution and to reversal potential models of neuronal behavior.
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作者：van den Berg, J.; Gandolfi, A.
作者单位：University of Rome Tor Vergata
摘要：For binary random variables sigma(1), sigma(2), . . . , sigma(n) that satisfy the well-known FKG condition, we show that the variances and covariances satisfy Var(sigma(j))Cov(sigma(i), sigma(k)) >= Cov(sigma(i), sigma(j))Cov(sigma(i), sigma(k)), 1 <= i, j, k <= n. This generalizes and improves a result by Graham for ferromagnetic Ising models with nonnegative external fields.
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作者：Dai, J. G.
作者单位：University System of Georgia; Georgia Institute of Technology; University System of Georgia; Georgia Institute of Technology
摘要：It is now known that the usual traffic condition (the nominal load being less than 1 at each station) is not sufficient for stability for a multiclass open queueing network. Although there has been some progress in establishing the stability conditions for a multiclass network, there is no unified approach to this problem. In this paper, we prove that a queueing network is positive Harris recurrent if the corresponding fluid limit model eventually reaches zero and stays there regardless of the...
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作者：Sellke, Thomas M.
作者单位：Purdue University System; Purdue University
摘要：Suppose a box contains m balls, numbered from 1 to m. A random number of balls are drawn from the box, their numbers are noted and the balls are then returned to the box. This is done repeatedly, with the sample sizes being iid. Let X be the number of samples needed to see all the balls. This paper uses Markov-chain coupling to derive a simple but typically very accurate approximation for EX in terms of the sample size distribution. The approximation formula generalizes the formula found by Po...
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作者：Coffman, E. G., Jr.; Puhalskii, A. A.; Reiman, M. I.
作者单位：AT&T; Nokia Corporation; Nokia Bell Labs; Russian Academy of Sciences
摘要：In polling systems, M >= 2 queues are visited by a single server in cyclic order. These systems model such diverse applications as token-ring communication networks and cyclic production systems. We study polling systems with exhaustive service and zero switchover (walk) times. Under standard heavy-traffic assumptions and scalings, the total unfinished work converges to a one-dimensional reflected Brownian motion, whereas the workloads of individual queues change at a rate that becomes infinit...
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作者：Wormald, Nicholas C.
作者单位：University of Melbourne
摘要：General criteria are given to ensure that in a family of discrete random processes, given parameters exhibit convergence to the solution of a system of differential equations. As one application we consider random graph processes in which the maximum degree is bounded and show that the numbers of vertices of given degree exhibit this convergence as the total number of vertices tends to infinity. Two other applications are to random processes which generate independent sets of vertices in rando...
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作者：Akahori, Jiro
作者单位：University of Tokyo
摘要：In this paper we present an explicit form of the distribution function of the occupation time of a Brownian motion with a constant drift (if there is no drift, this is the well-known arc-sine law). We also define the alpha-percentile of the stock price and give an explicit form of the distribution function of this random variable. Using this explicit distribution, we calculate the price of a new type of path-dependent option, called the alpha-percentile option. This option was first introduced...
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作者：Glasserman, Paul; Kou, Shing-Gang
作者单位：Columbia University; Columbia University
摘要：We consider limits of first passage times to indexed families of nested sets in regenerative processes. The sets are exponentially rare, in the sense that the probability that the process reaches an indexed set in a cycle vanishes exponentially fast in the indexing parameter. Under appropriate formulations of this hypothesis, we prove strong laws, iterated logarithm laws and limits in distribution, both for the index of the rarest set reached in a cycle and for the time to reach a set. An inte...
