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作者：Dassios, Angelos
作者单位：University of London; London School Economics & Political Science
摘要：The study of the quantile of a Brownian motion with a drift is undertaken. An explicit formula for its density, as well as a representation of its distribution as the sum of the maximum and the minimum of two resealed independent Brownian motions with drift, is given. The result is used in the pricing of a financial path-dependent option due to Miura.
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作者：Funaki, T.; Surgailis, D.; Woyczynski, W. A.
作者单位：Nagoya University; Vilnius University; University System of Ohio; Case Western Reserve University; University System of Ohio; Case Western Reserve University
摘要：We study the large time behavior of random fields which are solutions of a nonlinear partial differential equation, called Burgers' equation, under stochastic initial conditions. These are assumed to be of the shot noise type with the Gibbs-Cox process driving the spatial distribution of the bumps. In certain cases, this work extends an earlier effort by Surgailis and Woyczynski, where only noninteracting bumps driven by the traditional doubly stochastic Poisson process were considered. In con...
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作者：Bose, A.; Kaj, I.
作者单位：Carleton University; Uppsala University
摘要：We prove a diffusion limit theorem in the sense of weak convergence of measure-valued processes for a population age model first studied by Kendall. We show that in the diffusion limit scaling, the population structured in age groups behaves in the same way as the total population size, but with an exponential weight. A particular feature of the limiting process is that in general it is discontinuous at time zero.
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作者：Rhee, WanSoo T.
作者单位：University System of Ohio; Ohio State University
摘要：We give a unified simple proof of recent results of Alexander concerning the rate of convergence of the mean length of the longest common subsequence of two random sequences and the rate of convergence of the expected value of certain passage times in percolation theory.
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作者：Meyn, Sean P.
作者单位：University of Illinois System; University of Illinois Urbana-Champaign
摘要：This paper treats transience for queueing network models by considering an associated fluid limit model. If starting from any initial condition the fluid limit model explodes at a linear rate, then the associated queueing network with i.i.d. service times and a renewal arrival process explodes faster than any fractional power.
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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...
