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作者：van Handel, Ramon
作者单位：Princeton University
摘要：A hidden Markov model is called observable if distinct initial laws give rise to distinct laws of the observation process. Observability implies stability of the nonlinear filter when the signal process is tight, but this need not be the case when the signal process is unstable. This paper introduces a stronger notion of uniform observability which guarantees stability of the nonlinear filter in the absence of stability assumptions on the signal. By developing certain uniform approximation pro...
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作者：Durrett, Rick
作者单位：Cornell University
摘要：In this paper I will review twenty years of work on the question: When is there coexistence in stochastic spatial models? The answer, announced in Durrett and Levin [Theor Pop. Biol. 46 (1994) 363-394], and that we explain in this paper is that this can be determined by examining the mean-field ODE. There are a number of rigorous results in support of this picture, but we will state nine challenging and important open problems, most of which date from the 1990's.
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作者：Seierstad, Taral Guldahl
作者单位：University of Oslo
摘要：In a paper from 1995, Wormald gave general criteria for certain parameters in a family of discrete random processes to converge to the solution of a system of differential equations. Based on this method, we show that if some further conditions are satisfied, the parameters converge to a multivariate normal distribution.
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作者：Talreja, Rishi; Whitt, Ward
作者单位：Columbia University
摘要：We establish heavy-traffic stochastic-process limits for waiting times in many-server queues with customer abandonment. If the system is asymptotically critically loaded, as in the quality-and-efficiency-driven (QED) regime, then a bounding argument shows that the abandonment does not affect waiting-time processes. If instead the system is overloaded, as in the efficiency-driven (ED) regime, following Mandelbaum et al. [Proceedings of the Thirty-Seventh Annual Allerton Conference on Communicat...
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作者：Mandjes, Michel; Norros, Ilkka; Glynn, Peter
作者单位：University of Amsterdam; Stanford University; VTT Technical Research Center Finland
摘要：With M(t) := sup(s is an element of[0,t]) A(s) - s denoting the running maximum of a fractional Brownian motion A(.) with negative drift, this paper studies the rate of convergence of P(M(t) > x) to P(M > x). We define two metrics that measure the distance between the (complementary) distribution functions P(M(t) > .) and P(M > .). Our main result states that both metrics roughly decay as exp(-vt(2-2H)), where v is the decay rate corresponding to the tail distribution of the busy period in an ...
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作者：Cranston, M.; Gauthier, D.; Mountford, T. S.
作者单位：University of California System; University of California Irvine; Swiss Federal Institutes of Technology Domain; Ecole Polytechnique Federale de Lausanne
摘要：The focus of this article is on the different behavior of large deviations of random subadditive functionals above the mean versus large deviations below the mean in two random media models. We consider the point-to-point first passage percolation time a(n) on Z(d) and a last passage percolation time Z(n). For these functionals, we have lim(n ->infinity) a(n)/n = v and lim(n ->infinity) Z(n)/n = mu. Typically, the large deviations for such functionals exhibits a strong asymmetry, large deviati...
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作者：Reed, Josh
作者单位：New York University
摘要：In this paper, we study the G/GI/N queue in the Hallin-Whitt regime. Our first result is to obtain a deterministic fluid limit for the properly centered and scaled number of customers in the system which may be used to provide a first-order approximation to the queue length process. Our second result is to obtain a second-order stochastic approximation to the number of customers in the system in the Halfin-Whitt regime. This is accomplished by first centering the queue length process by its de...
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作者：Caravenna, Francesco; Petrelis, Nicolas
作者单位：University of Padua
摘要：We consider a model for a polymer chain interacting with a sequence of equispaced flat interfaces through a pinning potential. The intensity delta is an element of R of the pinning interaction is constant, while the interface spacing T = T(N) is allowed to vary with the size N of the polymer. Our main result is the explicit determination of the scaling behavior of the model in the large N limit, as a function of (T(N))(N) and for fixed delta > 0. In particular, we show that a transition occurs...
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作者：Lanchier, N.; Neuhauser, C.
作者单位：Arizona State University; Arizona State University-Tempe; University of Minnesota System; University of Minnesota Twin Cities
摘要：We introduce a spatially explicit model for the competition between type a and type b alleles. Each vertex of the d-dimensional integer lattice is occupied by a diploid individual, which is in one of three possible states or genotypes: an, ab or bb. We are interested in the long-term behavior of the gene frequencies when Mendel's law of segregation does not hold. This results in a voter type model depending on four parameters; each of these parameters measures the strength of competition betwe...
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作者：Gouere, Jean-Baptiste
作者单位：Universite de Orleans
摘要：We consider some continuum percolation models. We are mainly interested in giving some sufficient conditions for the absence of percolation. We give some general conditions and then focus on two examples. The first one is a multiscale percolation model based on the Boolean model. It was introduced by Meester and Roy and subsequently studied by Menshikov, Popov and Vachkovskaia. The second one is based on the stable marriage of Poisson and Lebesgue introduced by Hoffman, Holroyd and Peres and w...
