-
作者：Klenke, Achim; Mytnik, Leonid
作者单位：Johannes Gutenberg University of Mainz; Technion Israel Institute of Technology
摘要：Consider the mutually catalytic branching process with finite branching rate gamma We show that as gamma -> infinity, this process converges in finite-dimensional distributions (in time) to a certain discontinuous process. We give descriptions of this process in terms of its semigroup in terms of the infinitesimal generator and as the solution of a martingale problem We also give a strong construction in terms of a planar Brownian motion from which we infer a path property of the process This ...
-
作者：Goldstein, Larry
作者单位：University of Southern California
摘要：Let X-1, X-n be independent with zero means, finite variances sigma(2)(1), sigma(2)(n) and finite absolute third moments Let F-n be the distribution function of (X-1 + + X-n)/sigma where sigma(2) = Sigma(n)(t=1) sigma(2)(t), and Phi that of the standard normal The L-1-distance between F-n and Phi then satisfies parallel to F-n-Phi parallel to(1) <= 1/sigma(3) (n)Sigma E-t=1 vertical bar X-t vertical bar(3) In particular, when X-1. X-n are identically distributed with variance sigma(2). we have...
-
作者：Kuwae, Kazuhiro
作者单位：Kumamoto University
摘要：We refine stochastic calculus for symmetric Markov processes without using time reverse operators Under some conditions on the jump functions of locally square integrable martingale additive functionals, we extend Nakao's divergence-like continuous additive functional of zero energy and the stochastic integral with respect to It under the law for quasi-everywhere starting points, which are refinements of the previous results under the law for almost everywhere starting points This refinement o...
-
作者：Trapman, Pieter
作者单位：Stockholm University
摘要：We consider long-range percolation on Z(d), where the probability that two vertices at distance r are connected by an edge is given by p(r) = 1 - exp[-lambda(r)] is an element of (0, 1) and the presence or absence of different edges are independent Here, lambda(r) is a strictly positive, nonincreasing, regularly varying function We investigate the asymptotic growth of the size of the k-ball around the origin, vertical bar B(k)vertical bar, that is, the number of vertices that ale within graphd...
-
作者：Hsu, Elton P.; Qin, Guangnan
作者单位：Northwestern University; Chinese Academy of Sciences; Academy of Mathematics & System Sciences, CAS
摘要：We give an effective upper escape rate function for Brownian motion on a complete Riemannian manifold in terms of the volume growth of the manifold. An important step in the work is estimating the small tail probability of the crossing time between two concentric geodesic spheres by reflecting Brownian motions on the larger geodesic ball.
-
作者：Barany, Imre; Reitzner, Matthias
作者单位：Hungarian Academy of Sciences; HUN-REN; HUN-REN Alfred Renyi Institute of Mathematics; University of London; University College London; University Osnabruck
摘要：We prove the central limit theorem for the volume and the f-vector of the Poisson random polytope Pi(eta) in a fixed convex polytope P subset of R(d) Here, Pi(eta) is the convex hull of the intersection of a Poisson process X of intensity eta with P
-
作者：Komorowski, Tomasz; Peszat, Szymon; Szarek, Tomasz
作者单位：Maria Curie-Sklodowska University; Polish Academy of Sciences; Institute of Mathematics of the Polish Academy of Sciences; Polish Academy of Sciences; Institute of Mathematics of the Polish Academy of Sciences; Fahrenheit Universities; University of Gdansk
摘要：We formulate a criterion for the existence and uniqueness of an invariant measure for a Markov process taking values in a Polish phase space In addition. weak-* ergodicity, that is, the weak convergence of the ergodic averages of of the laws of the process starting from any initial distribution, is established The principal assumptions are the existence of a lower bound for the ergodic averages of the transition probability function and its local uniform continuity The latter is called the e-p...
-
作者：Wang, Jiun-Chau
作者单位：Queens University - Canada
摘要：In this paper, we study the superconvergence phenomenon in the free central limit theorem for identically distributed, unbounded summands We prove not only the uniform convergence of the densities to the semicircular density but also their L-P-convergence to the same limit for p > 1/2 Moreover, an entropic central limit theorem is obtained as a consequence of the above results
-
作者：Adams, Terrence M.; Nobel, Andrew B.
作者单位：United States Department of Defense; University of North Carolina; University of North Carolina Chapel Hill
摘要：We show that if X is a complete separable metric space and C is a countable family of Borel subsets of X with finite VC dimension, then, for every stationary ergodic process with values in X, the relative frequencies of sets C is an element of C converge uniformly to their limiting probabilities Beyond ergodicity. no assumptions are imposed on the sampling process. and no regularity conditions are imposed on the elements of C The result extends existing work of Vapnik and Chervonenkis among ot...
-
作者：Gotze, Friedrich; Tikhomirov, Alexander
作者单位：University of Bielefeld; Saint Petersburg State University
摘要：We consider the joint distribution of real and imaginary parts of eigen-values of random matrices with Independent entries with mean zero and unit variance We prove the convergence of this distribution to the uniform distribution on the unit disc without assumptions on the existence of a density for the distribution of entries We assume that the entries have a finite moment of order larger than two and consider the case of sparse matrices The results are based on previous work of Bai, Rudelson...
