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作者：Mountford, T.; Prabhakar, B.
作者单位：University of California System; University of California Los Angeles; University of California System; University of California Los Angeles
摘要：In this note we observe that the recent argument of Ekhaus and Gray combined with the approach of Liggett and Shiga shows that the limit from passing a stationary ergodic arrival process of rate alpha < 1 through a sequence of independent, rate one, exponential server queues is a Poisson process of rate alpha. This builds on work of Liggett and Shiga and Anantharam.
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作者：McDiarmid, Colin
作者单位：University of Oxford
摘要：We consider a branching random walk on the real line, with mean family size greater than 1. Let B-n denote the minimal position of a member of the nth generation. It is known that (under a weak condition) there is a finite constant gamma, defined in terms of the distributions specifying the process, such that as n -> infinity, we have B-n = gamma n + o(n) a.s. on the event S of ultimate survival. Our results here show that (under appropriate conditions), on S the random variable B-n is strongl...
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作者：Niemiro, Wojciech; Pokarowski, Piotr
作者单位：University of Warsaw; Polish Academy of Sciences; Institute of Mathematics of the Polish Academy of Sciences
摘要：We consider finite state nonhomogeneous Markov chains with one-step transition probabilities roughly proportional to powers of a small parameter, converging to zero. We examine asymptotic properties of trajectories. The analysis is based on the so-called orders of recurrence. Transient states, recurrent classes and periodic subclasses can be identified in terms of the matrix of powers. This leads to a complete description of the tail sigma field. Our theorems generalize the classical results f...
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作者：Stein, Michael L.
作者单位：University of Chicago
摘要：Consider predicting an integral of a stochastic process based on n observations of the stochastic process. Among all linear predictors, an optimal quadrature rule picks the n observation locations and the weights assigned to them to minimize the mean squared error of the prediction. While optimal quadrature rules are usually unattainable, it is possible to find rules that have good asymptotic properties as n -> infinity. Previous work has considered processes whose local behavior is like m-fol...
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作者：Gnedin, Alexander V.; Krengel, Ulrich
作者单位：University of Gottingen
摘要：We study the following two-person zero-sum game. n random numbers are drawn independently from a continuous distribution known to both players. Player 2 observes all the numbers and selects an order to present them to the opponent. Player 1 learns the numbers sequentially as they are presented and may stop learning whenever he/she pleases. If the stop occurred at the number that is the kth largest among all n numbers, Player 1 pays the amount q(k) to Player 2, where q(1) <= ... <= q(n) is a gi...
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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：Francos, Joseph M.; Meiri, A. Zvi; Porat, Boaz
作者单位：Ben-Gurion University of the Negev; Technion Israel Institute of Technology
摘要：Imposing a total order on a regular two-dimensional discrete random field induces an orthogonal decomposition of the random field into two components: a purely indeterministic field and a deterministic field. The deterministic component is further orthogonally decomposed into a half-plane deterministic field and a countable number of mutually orthogonal evanescent fields. Each of the evanescent fields is generated by the column-to-column innovations of the deterministic field with respect to a...
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作者：Dinwoodie, I. H.
作者单位：Tulane University
摘要：A bound is given for a reversible Markov chain on the probability that the occupation measure of a set exceeds the stationary probability of the set by a positive quantity.
