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作者：Raimond, Olivier
作者单位：Universite Paris Saclay
摘要：We study asymptotic properties of processes X, living in a Riemannian compact manifold M, solution of the stochastic differential equation (SDE) dX(t) = dW(t)(X-t) - beta(t)del V mu(t)(X-t)dt with W a Brownian vector field, beta(t) = a log(t + 1), mu(t) = 1/t integral(t)(0) delta(Xs)ds and V mu(t)(x) = 1/t integral(t)(0) V(x, X-s)ds, V being a smooth function. We show that the asymptotic behavior of mu(t) can be described by a non-autonomous differential equation. This class of processes exten...
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作者：Hu, Yaozhong; Nualart, David
作者单位：University of Kansas
摘要：The aim of this paper is to study the d-dimensional stochastic heat equation with a multiplicative Gaussian noise which is white in space and has the covariance of a fractional Brownian motion with Hurst parameter H is an element of (0,1) in time. Two types of equations are considered. First we consider the equation in the Ito-Skorohod sense, and later in the Stratonovich sense. An explicit chaos expansion for the solution is obtained. On the other hand, the moments of the solution are express...
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作者：Talagrand, Michel
作者单位：Universite Paris Cite; Sorbonne Universite
摘要：Given numbers a(ij) >= 0 for 1 <= i < j <= N, and given numbers b(i) >= 0, i <= N, we consider the random Hamiltonian Sigma(i, j <= N) root a(ij)g(ij)sigma(i)sigma(j) + Sigma(i <= N) root b(i)g(i)sigma(i), where g(i), g(ij) denote independent standard normal r.v., and where sigma(i) = +/- 1. We give sufficient conditions on the coefficients a(ij) for the system governed by this Hamiltonian to exhibit high-temperature behavior. There results extend known facts concerning the behavior of the She...
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作者：Mueller, Ursula U.; Schick, Anton; Wefelmeyer, Wolfgang
作者单位：State University of New York (SUNY) System; Binghamton University, SUNY; Texas A&M University System; Texas A&M University College Station; University of Cologne
摘要：We prove a Bahadur representation for a residual-based estimator of the innovation distribution function in a nonparametric autoregressive model. The residuals are based on a local linear smoother for the autoregression function. Our result implies a functional central limit theorem for the residual-based estimator.
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作者：Greven, Andreas; Pfaffelhuber, Peter; Winter, Anita
作者单位：University of Erlangen Nuremberg; University of Freiburg
摘要：We consider the space of complete and separable metric spaces which are equipped with a probability measure. A notion of convergence is given based on the philosophy that a sequence of metric measure spaces converges if and only if all finite subspaces sampled from these spaces converge. This topology is metrized following Gromov's idea of embedding two metric spaces isometrically into a common metric space combined with the Prohorov metric between probability measures on a fixed metric space....
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作者：Borodin, Alexei; Olshanski, Grigori
作者单位：California Institute of Technology; Kharkevich Institute for Information Transmission Problems of the RAS
摘要：Starting with finite Markov chains on partitions of a natural number n we construct, via a scaling limit transition as n -> az, a family of infinite-dimensional diffusion processes. The limit processes are ergodic; their stationary distributions, the so-called z-measures, appeared earlier in the problem of harmonic analysis for the infinite symmetric group. The generators of the processes are explicitly described.
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作者：Jiang, Tiefeng
作者单位：University of Minnesota System; University of Minnesota Twin Cities
摘要：We develop a tool to approximate the entries of a large dimensional complex Jacobi ensemble with independent complex Gaussian random variables. Based on this and the author's earlier work in this direction, we obtain the Tracy-Widom law of the largest singular values of the Jacobi emsemble. Moreover, the circular law, the Marchenko-Pastur law, the central limit theorem, and the laws of large numbers for the spectral norms are also obtained.
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作者：Kuwada, Kazumasa
作者单位：Ochanomizu University
摘要：We prove a precision of large deviation principle for current-valued processes such as shown in Bolthausen et al. (Ann Probab 23(1):236-267, 1995) for mean empirical measures. The class of processes we consider is determined by the martingale part of stochastic line integrals of 1-forms on a compact Riemannian manifold. For the pair of the current-valued process and mean empirical measures, we give an asymptotic evaluation of a nonlinear Laplace transform under a nondegeneracy assumption on th...
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作者：Baraud, Yannick; Birge, Lucien
作者单位：Sorbonne Universite; Universite Paris Cite; Universite Cote d'Azur
摘要：The purpose of this paper is to estimate the intensity of some random measure N on a set X by a piecewise constant function on a finite partition of X. Given a (possibly large) family M of candidate partitions, we build a piecewise constant estimator (histogram) on each of them and then use the data to select one estimator in the family. Choosing the square of a Hellinger-type distance as our loss function, we show that each estimator built on a given partition satisfies an analogue of the cla...
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作者：Kallenberg, Olav
作者单位：Auburn University System; Auburn University
摘要：For simple point processes xi on a Borel space S, we prove some approximations involving conditional distributions, given that xi hits a small set B. Beginning with general versions of some classical limit theorems, going back to the pioneering work of Palm and Khinchin, we proceed to prove that, under suitable regularity conditions, the contributions to B and B-c are asymptotically conditionally independent. We further derive approximations in total variation of reduced Palm distributions and...
