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作者：Duffy, James A.
作者单位：University of Oxford; University of Oxford
摘要：We provide a uniform law for the weak convergence of additive functionals of partial sum processes to the local times of linear fractional stable motions, in a setting sufficiently general for statistical applications. Our results are fundamental to the analysis of the global properties of nonparametric estimators of nonlinear statistical models that involve such processes as covariates.
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作者：Bhattacharya, Bhaswar B.
作者单位：Stanford University
摘要：Consider an urn model where at each step one of q colors is sampled according to some probability distribution and a ball of that color is placed in an urn. The distribution of assigning balls to urns may depend on the color of the ball. Collisions occur when a ball is placed in an urn which already contains a ball of different color. Equivalently, this can be viewed as sequentially coloring a complete q-partite graph wherein a collision corresponds to the appearance of a monochromatic edge. U...
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作者：Douc, Randal; Roueff, Francois; Sim, Tepmony
作者单位：Centre National de la Recherche Scientifique (CNRS); IMT - Institut Mines-Telecom; Institut Polytechnique de Paris; Telecom SudParis; IMT - Institut Mines-Telecom; Institut Polytechnique de Paris; Telecom Paris; Centre National de la Recherche Scientifique (CNRS); Universite Paris Saclay
摘要：This paper deals with a parametrized family of partially observed bivariate Markov chains. We establish that, under very mild assumptions, the limit of the normalized log-likelihood function is maximized when the parameters belong to the equivalence class of the true parameter, which is a key feature for obtaining the consistency of the maximum likelihood estimators (MLEs) in well-specified models. This result is obtained in the general framework of partially dominated models. We examine two s...
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作者：Edelman, Alan; Guionnet, A.; Peche, S.
作者单位：Massachusetts Institute of Technology (MIT); Universite Paris Cite
摘要：In order to have a better understanding of finite random matrices with non-Gaussian entries, we study the 1/N expansion of local eigenvalue statistics in both the bulk and at the hard edge of the spectrum of random matrices. This gives valuable information about the smallest singular value not seen in universality laws. In particular, we show the dependence on the fourth moment (or the kurtosis) of the entries. This work makes use of the so-called complex Gaussian divisible ensembles for both ...
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作者：Crane, Harry
作者单位：Rutgers University System; Rutgers University New Brunswick
摘要：We study a broad class of stochastic process models for dynamic networks that satisfy the minimal regularity conditions of (i) exchangeability and (ii) cadlag sample paths. Our main theorems characterize these processes through their induced behavior in the space of graph limits. Under the assumption of time-homogeneous Markovian dependence, we classify the dis-continuities of these processes into three types, prove bounded variation of the sample paths in graph limit space and express the pro...
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作者：Griffin, Philip S.
作者单位：Syracuse University
摘要：Recent studies have demonstrated an interesting connection between the asymptotic behavior at ruin of a Levy insurance risk process under the Cramer-Lundberg and convolution equivalent conditions. For example, the limiting distributions of the overshoot and the undershoot are strikingly similar in these two settings. This is somewhat surprising since the global sample path behavior of the process under these two conditions is quite different. Using tools from excursion theory and fluctuation t...
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作者：Gruebel, Rudolf; Kabluchko, Zakhar
作者单位：Leibniz University Hannover; University of Munster
摘要：Let W-infinity (beta) be the limit of the Biggins martingale W-n(beta) associated to a supercritical branching random walk with mean number of offspring m. We prove a functional central limit theorem stating that as n -> infinity the process D-n(u) := m(1/2n) (W-infinity(u/root n) - W-n(u/root n)) converges weakly, on a suitable space of analytic functions, to a Gaussian random analytic function with random variance. Using this result, we prove central limit theorems for the total path length ...
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作者：Cerny, Jeri; Teixeira, Augusto
作者单位：University of Vienna
摘要：For d >= 3, we construct a new coupling of the trace left by a random walk on a large d-dimensional discrete torus with the random interlacements on Z(d). This coupling has the advantage of working up to macroscopic subsets of the torus. As an application, we show a sharp phase transition for the diameter of the component of the vacant set on the torus containing a given point. The threshold where this phase transition takes place coincides with the critical value u star(d) of random interlace...
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作者：Zhang, Xicheng
作者单位：Wuhan University
摘要：In this paper, we study properties of solutions to stochastic differential equations with Sobolev diffusion coefficients and singular drifts. The properties we study include stability with respect to the coefficients, weak differentiability with respect to starting points and the Malliavin differentiability with respect to sample paths. We also establish Bismut-Elworthy-Li's formula for the solutions. As an application, we use the stochastic Lagrangian representation of incompressible Navier-S...
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作者：Torrisi, Giovanni Luca
作者单位：Consiglio Nazionale delle Ricerche (CNR); Istituto per le Applicazioni del Calcolo Mauro Picone (IAC-CNR)
摘要：We give a general Gaussian bound for the first chaos (or innovation) of point processes with stochastic intensity constructed by embedding in a bivariate Poisson process. We apply the general result to nonlinear Hawkes processes, providing quantitative central limit theorems.
