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作者：Lahiri, S. N.; Sun, S.
作者单位：Texas A&M University System; Texas A&M University College Station; University System of Ohio; Wright State University Dayton
摘要：This paper proves a Berry-Esseen theorem for sample quantiles of strongly-mixing random variables under a polynomial mixing rate. The rate of normal approximation is shown to be O(n(-1/2)) as n -> infinity, where n denotes the sample size. This result is in sharp contrast to the case of the sample mean of strongly-mixing random variables where the rate O(n-1/2) is not known even under an exponential strong mixing rate. The main result of the paper has applications in finance and econometrics a...
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作者：Dolera, Emanuele; Gabetta, Ester; Regazzini, Eugenio
作者单位：University of Pavia
摘要：Let f (.,t) be the probability density function which represents the solution of Kac's equation at time t, with initial data f(0), and let g(sigma) be the Gaussian density with zero mean and variance sigma(2), sigma(2) being the value of the second moment of f(0). This is the first study which proves that the total variation distance between f(., t) and g(sigma) goes to zero, as t ->+infinity, with an exponential rate equal to -1/4. In the present paper, this fact is proved on the sole assumpt...
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作者：Pra, Paolo Dai; Runggaldier, Wolfgang J.; Sartori, Elena; Tolotti, Marco
作者单位：University of Padua; Bocconi University; Scuola Normale Superiore di Pisa; Universita Ca Foscari Venezia
摘要：Using particle system methodologies we study the propagation of financial distress in a network of firms facing credit risk, We investigate the phenomenon of a credit crisis and quantify the losses that a bank may suffer in a large credit portfolio. Applying a large deviation principle we compute the limiting distributions of the system and determine the time evolution of the credit quality indicators of the firms, deriving moreover the dynamics of a global financial health indicator. We final...
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作者：Baryshnikov, Yu.; Penrose, Mathew D.; Yukichi, J. E.
作者单位：Alcatel-Lucent; Lucent Technologies; AT&T; University of Bath; Lehigh University
摘要：Nearest neighbor cells in R-d, d is an element of N, are used to define coefficients of divergence (phi-divergences) between continuous multivariate samples. For large sample sizes, such distances are shown to be asymptotically normal with a variance depending on the underlying point density. In d = 1, this extends classical central limit theory for sum functions of spacings. The general results yield central limit theorems for logarithmic k-spacings, information gain, log-likelihood ratios an...
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作者：Dyer, Martin; Goldberg, Leslie Ann; Jerrum, Mark
作者单位：University of Leeds; University of Liverpool; University of London
摘要：We give a systematic development of the application of matrix norms to rapid mixing in spin systems. We show that rapid mixing of both random update Glauber dynamics and systematic scan Glauber dynamics occurs if any matrix norm or the associated dependency matrix is less than 1. We give improved analysis for the case in which the diagonal of the dependency matrix is 0 (as in heat bath dynamics). We apply the matrix norm methods to random update and systematic scan Glauber dynamics for colorin...
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作者：Yakovlev, Andrei Y.; Yanev, Nikolay M.
作者单位：University of Rochester; Bulgarian Academy of Sciences
摘要：This paper considers the relative frequencies of distinct types of individuals in multitype branching processes. We prove that the frequencies are asymptotically multivariate normal when the initial number of ancestors is large and the time of observation is fixed. The result is valid for any branching process with a finite number of types; the only assumption required is that of independent individual evolutions. The problem under consideration is motivated by applications in the area of cell...
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作者：Holden, Lars; Hauge, Ragnar; Holden, Marit
摘要：We propose an adaptive independent Metropolis-Hastings algorithm with the ability to learn from all previous proposals in the chain except the current location. It is an extension of the independent Metropolis-Hastings algorithm. Convergence is proved provided a strong Doeblin condition is satisfied, which essentially requires that all the proposal functions have uniformly heavier tails than the stationary distribution. The proof also holds if proposals depending on the current state are used ...
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作者：Teixeira, Augusto
作者单位：Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：We consider the model of random interlacements on Z(d) introduced in Sznitman [Vacant set of random interlacements and percolation (2007) preprint]. For this model, we prove the uniqueness of the infinite component of the vacant set. As a consequence, we derive the continuity in a of the probability that the origin belongs to the infinite component of the vacant set at level a in the supercritical phase u < u*.
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作者：Durrett, Rick; Popovic, Lea
作者单位：Cornell University; Concordia University - Canada
摘要：We consider two processes that have been used to study gene duplication, Watterson's [Genetics 105 (1983) 745-766] double recessive null model and lynch and Force's [Genetics 154 (2000) 459-473] subfunctionalization model. Though the state spaces of these diffusions are two and six-dimensional, respectively, we show in each case that the diffusion stays close to a curve. Using ideas of Katzenberger [Ann. Probab. 19 (1991) 1587-1628] we show that one-dimensional projections converge to diffusio...
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作者：Gromoll, H. Christian; Williams, Ruth J.
作者单位：University of Virginia; University of California System; University of California San Diego
摘要：We consider a stochastic model of Internet congestion control, introduced by Massoulie and Roberts [telecommunication Systems 15 (2000) 185-201], that represents the randomly varying number of flows in a network where bandwidth is shared among document transfers. In contrast to an ear lier work by Kelly and Williams [Ann. Appl. Probab. 14 (2004) 1055-1083], the present paper allows interarrival times and document sires to be generally distributed, rather than exponentially distributed. Further...
