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作者：Chen, Hong
作者单位：University of British Columbia
摘要：This paper studies the fluid approximation (also known as the functional strong law of large numbers) and the stability (positive Harris recurrence) for a multiclass queueing network. Both of these are related to the stabilities of a linear fluid model, constructed from the first-order parameters (i.e., long-run average arrivals, services and routings) of the queueing network. It is proved that the fluid approximation for the queueing network exists if the corresponding linear fluid model is w...
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作者：Pitt, Loren D.; Robeva, Raina; Wang, Da Yi
作者单位：University of Virginia; National University of Singapore
摘要：For a wide sense stationary random field Phi = {phi(x): x is an element of R-2}, we investigate the asymptotic errors made in the numerical integration of line intergrals of the form integral(Gamma) f(x)phi(x)d sigma(x). It is shown, for example, that if f and Gamma are smooth, and if the spectral density rho(lambda) satisfies rho(lambda) approximate to k vertical bar lambda vertical bar(-4) as lambda -> infinity, then there is a constant c' with (NE)-E-3 vertical bar integral(Gamma) f(x)phi(x...
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作者：Liggett, Thomas M.
作者单位：University of California System; University of California Los Angeles
摘要：We prove survival for a class of discrete time Markov processes whose states are finite sets of integers. As applications, we obtain upper bounds for the critical values of various two-dimensional oriented percolation models. The technique of proof is based generally on that used by Holley and Liggett to prove survival of the one-dimensional basic contact process. However, the fact that our processes evolve in discrete time requires that we make substantial changes in the way this technique is...
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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：Brightwell, Graham; Ott, Teunis J.; Winkler, Peter
作者单位：University of London; London School Economics & Political Science; Telcordia Technologies; Nokia Corporation; Nokia Bell Labs; AT&T
摘要：We consider the following distributed optimization problem: Given a set X-1, ..., X-n of pairwise independent random variables and a target value T, a subset of the X-i's must be selected whose sum is close to T. However, no cooperation is permitted in determining the set; each variable must be programmed in advance, joining or not joining according to its own value. Such conditions may arise, for example, when supply of some commodity is controlled at several random sources. Under these gener...
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作者：Kuensch, Hans; Geman, Stuart; Kehagias, Athanasios
作者单位：Swiss Federal Institutes of Technology Domain; ETH Zurich; Brown University; Aristotle University of Thessaloniki
摘要：A noninvertible function of a first-order Markov process or of a nearest-neighbor Markov random field is called a hidden Markov model. Hidden Markov models are generally not Markovian. In fact, they may have complex and long range interactions, which is largely the reason for their utility. Applications include signal and image processing, speech recognition and biological modeling. We show that hidden Markov models are dense among essentially all finite-state discrete-time stationary processe...
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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...
