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作者：Eder, Irmingard; Klueppelberg, Claudia
作者单位：Technical University of Munich; Technical University of Munich
摘要：For the sum process X = X-1 + X-2 of a bivariate Levy process (X-1, X-2) with possibly dependent components, we derive a quintuple law describing the first upwards passage event of X over a fixed barrier, caused by a jump, by the joint distribution of five quantities: the time relative to the time of the previous maximum, the time of the previous maximum, the overshoot, the undershoot and the undershoot of the previous maximum. The dependence between the jumps of X-1 and X-2 is modeled by a Le...
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作者：Cotar, Codina; Limic, Vlada
作者单位：Technical University of Berlin; Centre National de la Recherche Scientifique (CNRS)
摘要：We consider a class of strongly edge-reinforced random walks, where the corresponding reinforcement weight function is nondecreasing. It is known, from Limic and Tarres [Ann. Probab. (2007), to appear], that the attracting edge emerges with probability I whenever the underlying graph is locally bounded. We study the asymptotic behavior of the tail distribution of the (random) time of attraction. In particular, we obtain exact (up to a multiplicative constant) asymptotics if the underlying grap...
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作者：Goldenshluger, Alexander; Zeevi, Assaf
作者单位：University of Haifa; Columbia University
摘要：We consider the one-armed bandit problem of Woodroofe [J. Amer Statist. Assoc. 74 (1979) 799-806], which involves sequential sampling from two populations: one whose characteristics are known, and one which depends on an unknown parameter and incorporates a covariate. The goal is to maximize cumulative expected reward. We study this problem in a minimax setting, and develop rate-optimal polices that involve suitable modifications of the myopic rule. It is shown that the regret, as well as the ...
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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：Graham, Carl; Robert, Philippe
作者单位：Institut Polytechnique de Paris; Ecole Polytechnique; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
摘要：The mean-field limit of a Markovian model describing the interaction of several classes of permanent connections in a network is analyzed. Each of the connections has a self-adaptive behavior in that its transmission rate along its route depends on the level of congestion of the nodes of the route. Since several classes of connections going through the nodes of the network are considered, an original mean-field result in a multi-class context is established. It is shown that, as the number of ...
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作者：Durrett, Rick; Remenik, Daniel
作者单位：Cornell University
摘要：We investigate an interacting particle system inspired by the gypsy moth, whose populations grow until they become sufficiently dense so that an epidemic reduces them to a low level. We consider this process on a random 3-regular graph and on the d-dimensional lattice and torus, with d >= 2. On the finite graphs with global dispersal or with a dispersal radius that grows with the number of sites, we prove convergence to a dynamical system that is chaotic for some parameter values. We conjectur...
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作者：Wu, Wei Biao
作者单位：University of Chicago
摘要：For statistical inference of means of stationary processes, one needs to estimate their time-average variance constants (TAVC) or long-run variances. For a stationary process, its TAVC is the sum of all its covariances and it is a multiple of the spectral density at zero. The classical TAVC estimate which is based on batched means does not allow recursive updates and the required memory complexity is O(n). We propose a faster algorithm which recursively computes the TAVC, thus having memory co...
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作者：Cerrai, Sandra
作者单位：University of Florence
摘要：We prove that an averaging principle holds for a general class of stochastic reaction-diffusion systems, having unbounded multiplicative noise, in any space dimension. We show that the classical Khasminskii approach for systems with a finite number of degrees of freedom can be extended to infinite-dimensional systems.
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作者：Heveling, Matthias; Reitzner, Matthias
作者单位：Technische Universitat Wien
摘要：Let X be a Poisson point process and K subset of R(d) a measurable set. Construct the Voronoi cells of all points x is an element of X with respect to X, and denote by v(X)(K) the union of all Voronoi cells with nucleus in K. For K a compact convex set the expectation of the volume difference V(v(X)(K)) - V(K) and the symmetric difference V(v(X)(K)Delta K) is computed. Precise estimates for the variance of both quantities are obtained which follow from a new jackknife inequality for the varian...
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作者：El Karoui, Noureddine
作者单位：University of California System; University of California Berkeley
摘要：We place ourselves in the setting of high-dimensional statistical inference, where the number of variables p in a data set of interest is of the same order of magnitude as the number of observations n. More formally, we study the asymptotic properties of correlation and covariance matrices, in the setting where p/n -> rho is an element of (0, infinity), for general population covariance. We show that, for a large class of models studied in random matrix theory, spectral properties of large-dim...
