6期

最新文章

• REGENERATIVE PROPERTIES OF THE LINEAR HAWKES PROCESS WITH UNBOUNDED MEMORY AI翻译
  作者：Graham, Carl
  作者单位：Institut Polytechnique de Paris; Ecole Polytechnique; Centre National de la Recherche Scientifique (CNRS)
  摘要：Regenerative properties of the linear Hawkes process are proved under minimal assumptions on the transfer function, which may have unbounded support. For this, an original construction of the Hawkes process as a functional of a Poisson point process is derived from the immigration-birth representation, and the independence properties of the Poisson point process are exploited to exhibit regeneration times which are anticipative and not even measurable w.r.t. the Hawkes process. The regeneratio...
• RECURRENCE OF TWO-DIMENSIONAL QUEUEING PROCESSES, AND RANDOM WALK EXIT TIMES FROM THE QUADRANT AI翻译
  作者：Peigne, Marc; Woess, Wolfgang
  作者单位：Centre National de la Recherche Scientifique (CNRS); Universite de Orleans; Universite de Tours; Graz University of Technology
  摘要：Let X = (X-1, X-2) be a two-dimensional random variable and X(n), n is an element of N, a sequence of i.i.d. copies of X. The associated random walk is S(n) = X(1)+ ... + X(n). The corresponding absorbed-reflected walk W(n), n is an element of N, in the first quadrant is given by W(0) = x is an element of R-+(2) and W(n) = max{0, W(n - 1) - X(n)}, where the maximum is taken coordinate-wise. This is often called the Lindley process and models the waiting times in a two-server queue. We characte...
• A WEAK SOLUTION THEORY FOR STOCHASTIC VOLTERRA EQUATIONS OF CONVOLUTION TYPE AI翻译
  作者：Jaber, Eduardo Abi; Cuchiero, Christa; Larsson, Martin; Pulido, Sergio
  作者单位：University of Vienna; Carnegie Mellon University; Ecole Nationale Superieure d'Informatique pour l'Industrie et l'Entreprise (ENSIIE); Universite Paris Saclay; Centre National de la Recherche Scientifique (CNRS)
  摘要：We obtain general weak existence and stability results for stochastic convolution equations with jumps under mild regularity assumptions, allowing for non-Lipschitz coefficients and singular kernels. Our approach relies on weak convergence in L-p spaces. The main tools are new a priori estimates on Sobolev-Slobodeckij norms of the solution, as well as a novel martingale problem that is equivalent to the original equation. This leads to generic approximation and stability theorems in the spirit...
• LARGE DEVIATIONS FOR THE EMPIRICAL MEASURE OF THE ZIG-ZAG PROCESS AI翻译
  作者：Bierkens, Joris; Nyquist, Pierre; Schlottke, Mikola C.
  作者单位：Delft University of Technology; Royal Institute of Technology; Eindhoven University of Technology
  摘要：The zig-zag process is a piecewise deterministic Markov process in position and velocity space. The process can be designed to have an arbitrary Gibbs type marginal probability density for its position coordinate, which makes it suitable for Monte Carlo simulation of continuous probability distributions. An important question in assessing the efficiency of this method is how fast the empirical measure converges to the stationary distribution of the process. In this paper we provide a partial a...
• RANDOMIZED HAMILTONIAN MONTE CARLO AS SCALING LIMIT OF THE BOUNCY PARTICLE SAMPLER AND DIMENSION-FREE CONVERGENCE RATES AI翻译
  作者：Deligiannidis, George; Paulin, Daniel; Bouchard-Cote, Alexandre; Doucet, Arnaud
  作者单位：University of Oxford; University of Edinburgh; University of British Columbia
  摘要：The bouncy particle sampler is a Markov chain Monte Carlo method based on a nonreversible piecewise deterministic Markov process. In this scheme, a particle explores the state space of interest by evolving according to a linear dynamics which is altered by bouncing on the hyperplane perpendicular to the gradient of the negative log-target density at the arrival times of an inhomogeneous poisson process (PP) and by randomly perturbing its velocity at the arrival times of a homogeneous PP. Under...
• BREAKING A CHAIN OF INTERACTING BROWNIAN PARTICLES AI翻译
  作者：Aurzada, Frank; Betz, Volker; Lifshits, Mikhail
  作者单位：Technical University of Darmstadt; Saint Petersburg State University
  摘要：We investigate the behaviour of a finite chain of Brownian particles, interacting through a pairwise linear force, with one end of the chain fixed and the other end pulled away at slow speed, in the limit of slow speed and small Brownian noise. We study the instant when the chain breaks, that is, the distance between two neighbouring particles becomes larger than a certain threshold. There are three different regimes depending on the relation between the speed of pulling and the Brownian noise...
• A SIMPLE FOURIER ANALYTIC PROOF OF THE AKT OPTIMAL MATCHING THEOREM AI翻译
  作者：Bobkov, Sergey G.; Ledoux, Michel
  作者单位：University of Minnesota System; University of Minnesota Twin Cities; Universite de Toulouse; Universite Toulouse III - Paul Sabatier
  摘要：We present a short and elementary proof of the Ajtai-Komlos-Tusnady (AKT) optimal matching theorem in dimension 2 via Fourier analysis and a smoothing argument. The upper bound applies to more general families of samples, including dependent variables, of interest in the study of rates of convergence for empirical measures. Following the recent pde approach by L. Ambrosio, F. Stra and D. Trevisan, we also adapt a simple proof of the lower bound.
• ASYMPTOTIC ANALYSIS FOR EXTREME EIGENVALUES OF PRINCIPAL MINORS OF RANDOM MATRICES AI翻译
  作者：Cai, T. Tony; Jiang, Tiefeng; Li, Xiaoou
  作者单位：University of Pennsylvania; University of Minnesota System; University of Minnesota Twin Cities
  摘要：Consider a standard white Wishart matrix with parameters n and p. Motivated by applications in high-dimensional statistics and signal processing, we perform asymptotic analysis on the maxima and minima of the eigenvalues of all the m x m principal minors, under the asymptotic regime that n, p, m go to infinity. Asymptotic results concerning extreme eigenvalues of principal minors of real Wigner matrices are also obtained. In addition, we discuss an application of the theoretical results to the...
• UNIVERSALITY FOR LANGEVIN-LIKE SPIN GLASS DYNAMICS AI翻译
  作者：Dembo, Amir; Lubetzky, Eyal; Zeitouni, Ofer
  作者单位：Stanford University; Stanford University; New York University; Weizmann Institute of Science
  摘要：We study dynamics for asymmetric spin glass models, proposed by Hertz et al. and Sompolinsky et al. in the 1980's in the context of neural networks: particles evolve via a modified Langevin dynamics for the Sherrington-Kirkpatrick model with soft spins, whereby the disorder is i.i.d. standard Gaussian rather than symmetric. Ben Arous and Guionnet (Probab. Theory Related Fields 102 (1995) 455-509), followed by Guionnet (Probab. Theory Related Fields 109 (1997) 183-215), proved for Gaussian inte...
• PALM THEORY, RANDOM MEASURES AND STEIN COUPLINGS AI翻译
  作者：Chen, Louis H. Y.; Rollin, Adrian; Xia, Aihua
  作者单位：National University of Singapore; National University of Singapore; University of Melbourne
  摘要：We establish a general Berry-Esseen type bound which gives optimal bounds in many situations under suitable moment assumptions. By combining the general bound with Palm theory, we deduce a new error bound for assessing the accuracy of normal approximation to statistics arising from random measures, including stochastic geometry. We illustrate the use of the bound in four examples: completely random measures, excursion random measure of a locally dependent random process, and the total edge len...