-
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.
-
作者：Marinucci, Domenico; Rossi, Maurizia; Vidotto, Anna
作者单位：University of Rome Tor Vergata; University of Milano-Bicocca; G d'Annunzio University of Chieti-Pescara
摘要：In this paper, we consider isotropic and stationary real Gaussian random fields defined on S-2 x R and we investigate the asymptotic behavior, as T -> +infinity, of the empirical measure (excursion area) in S-2 x [0, T] at any threshold, covering both cases when the field exhibits short and long memory, that is, integrable and nonintegrable temporal covariance. It turns out that the limiting distribution is not universal, depending both on the memory parameters and the threshold. In particular...
-
作者：Champagnat, Nicolas; Meleard, Sylvie; Viet Chi Tran
作者单位：Centre National de la Recherche Scientifique (CNRS); Universite de Lorraine; Centre National de la Recherche Scientifique (CNRS); Institut Polytechnique de Paris; Ecole Polytechnique; Universite Gustave-Eiffel; Universite Paris-Est-Creteil-Val-de-Marne (UPEC)
摘要：Horizontal gene transfer consists in exchanging genetic materials between microorganisms during their lives. This is a major mechanism of bacterial evolution and is believed to be of main importance in antibiotics resistance. We consider a stochastic model for the evolution of a discrete population structured by a trait taking finitely many values, with density-dependent competition. Traits are vertically inherited unless a mutation occurs, and can also be horizontally transferred by unilatera...
-
作者：Lyberopoulos, Demetrios P.; Macheras, Nikolaos D.
作者单位：University of Piraeus
摘要：If a given aggregate process S is a mixed compound Poisson process under a probability measure P, we provide a characterization of all probability measures Q on the domain of P, such that P and Q are progressively equivalent and S remains a mixed compound Poisson process with improved properties. This result generalizes earlier work of Delbaen and Haezendonck (Insurance Math. Econom. 8 (1989) 269-277). Implications related to the computation of premium calculation principles in an insurance ma...
-
作者：Ferrari, Patrik L.; Veto, Balint
作者单位：University of Bonn; Budapest University of Technology & Economics; MTA-BME Stochastics Research Group
摘要：We consider uniform random domino tilings of the restricted Aztec diamond which is obtained by cutting off an upper triangular part of the Aztec diamond by a horizontal line. The restriction line asymptotically touches the arctic circle that is the limit shape of the north polar region in the unrestricted model. We prove that the rescaled boundary of the north polar region in the restricted domain converges to the Airy(2) process conditioned to stay below a parabola with explicit continuous st...
-
作者：Last, Guenter; Nestmann, Franz; Schulte, Matthias
作者单位：Helmholtz Association; Karlsruhe Institute of Technology; Heriot Watt University
摘要：The random connection model is a random graph whose vertices are given by the points of a Poisson process and whose edges are obtained by randomly connecting pairs of Poisson points in a position dependent but independent way. We study first and second order properties of the numbers of components isomorphic to given finite connected graphs. For increasing observation windows in an Euclidean setting we prove qualitative multivariate and quantitative univariate central limit theorems for these ...
-
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...
-
作者：Bhattacharya, Bhaswar B.; Mukherjee, Somabha; Mukherjee, Sumit
作者单位：University of Pennsylvania; Columbia University
摘要：Consider the random quadratic form T-n = Sigma(1 <= u<= n) a(uv)X(u)X(v), where ((a(uv)))1(<= u,v <= n) is a {0, 1}-valued symmetric matrix with zeros on the diagonal, and X-1, X-2,..., X-n are i.i.d. Ber(p(n)), with p(n) is an element of (0, 1). In this paper, we prove various characterization theorems about the limiting distribution of T-n, in the sparse regime, where p(n) -> 0 such that E(T-n) = O(1). The main result is a decomposition theorem showing that distributional limits of Tn is the...
-
作者：Lambert, Amaury; Pina, Veronica Miro; Schertzer, Emmanuel
作者单位：Universite Paris Cite; Sorbonne Universite; Institut National de la Sante et de la Recherche Medicale (Inserm); Universite PSL; College de France
摘要：We consider a Moran model with recombination in a haploid population of size N. At each birth event, with probability 1-rho R-N the offspring copies one parent's chromosome, and with probability rho R-N she inherits a chromosome that is a mosaic of both parental chromosomes. We assume that at time 0 each individual has her chromosome painted in a different color and we study the color partition of the chromosome that is asymptotically fixed in a large population, when we look at a portion of t...
-
作者：Bender, Christian; Schweizer, Nikolaus
作者单位：Saarland University; Tilburg University
摘要：We propose a new least-squares Monte Carlo algorithm for the approximation of conditional expectations in the presence of stochastic derivative weights. The algorithm can serve as a building block for solving dynamic programming equations, which arise, for example, in nonlinear option pricing problems or in probabilistic discretization schemes for fully nonlinear parabolic partial differential equations. Our algorithm can be generically applied when the underlying dynamics stem from an Euler a...
