2期

最新文章

• NONLINEAR SEMIGROUPS AND LIMIT THEOREMS FOR CONVEX EXPECTATIONS AI翻译
  作者：Blessing, Jonas; Kupper, Michael
  作者单位：Swiss Federal Institutes of Technology Domain; ETH Zurich; University of Konstanz
  摘要：Based on the Chernoff approximation, we provide a general approximation result for convex monotone semigroups which are continuous w.r.t. the mixed topology on suitable spaces of continuous functions. Starting with a family (I (t))t >= 0 of operators, the semigroup is constructed as the limit S(t)f := limn ->infinity I (t/n)n f and is uniquely determined by the time derivative I'(0)f for smooth functions. We identify explicit conditions for the generating family (I (t))t >= 0 that are transfer...
• WEAK WELL-POSEDNESS OF STOCHASTIC VOLTERRA EQUATIONS WITH COMPLETELY MONOTONE KERNELS AND NONDEGENERATE NOISE AI翻译
  作者：Hamaguchi, Yushi
  作者单位：Kyoto University
  摘要：We establish weak existence and uniqueness in law for stochastic Volterra equations (SVEs for short) with completely monotone kernels and nondegenerate noise under mild regularity assumptions. In particular, our results reveal the regularization-by-noise effect for SVEs with singular kernels, allowing for multiplicative noise with H & ouml;lder diffusion coefficients. In order to prove our results, we reformulate the SVE into an equivalent stochastic evolution equation (SEE for short) defined ...
• SHARP ANALYSIS ON THE JOINT DISTRIBUTION OF THE NUMBER OF DESCENTS AND INVERSE DESCENTS IN A RANDOM PERMUTATION AI翻译
  作者：Bercu, Bernard; Bonnefont, Michel; Fredes, Luis; Richou, Adrien
  作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite de Bordeaux
  摘要：Chatterjee and Diaconis have recently shown the asymptotic normality for the joint distribution of the number of descents and inverse descents in a random permutation. A noteworthy point of their results is that the asymptotic variance of the normal distribution is diagonal, which means that the number of descents and inverse descents are asymptotically uncorrelated. The goal of this paper is to go further in this analysis by proving a large deviation principle for the joint distribution. We s...
• MACROSCOPIC DIFFUSIVE FLUCTUATIONS FOR GENERALIZED HARD RODS DYNAMICS AI翻译
  作者：Ferrari, Pablo A.; Olla, Stefano
  作者单位：University of Buenos Aires; Consejo Nacional de Investigaciones Cientificas y Tecnicas (CONICET); University of Buenos Aires; Universite PSL; Universite Paris-Dauphine; Institut Universitaire de France; Gran Sasso Science Institute (GSSI)
  摘要：We study the fluctuations in equilibrium for a dynamics of rods with random length. This includes the classical hard rod elastic collisions, when rod lengths are constant and equal to a positive value. We prove that in the diffusive space-time scaling, an initial fluctuation of density of particles of velocity v, after recentering on its Euler evolution, evolve randomly shifted by a Brownian motion of variance D(v).
• CENTRAL LIMIT THEOREM FOR GRAM-SCHMIDT RANDOM WALK DESIGN AI翻译
  作者：Chatterjee, Sabyasachi; Dey, Partha S.; Goswami, Subhajit
  作者单位：University of Illinois System; University of Illinois Urbana-Champaign; Tata Institute of Fundamental Research (TIFR)
  摘要：We prove a central limit theorem for the Horvitz-Thompson estimator based on the Gram-Schmidt walk (GSW) design, recently developed in Harconsider the version of GSW design, which uses a randomized pivot order. We deduce our result under very mild assumptions involving only the problem parameters, such as the (sum) potential outcome vector and the covariate matrix. As a very important consequence of our analysis, we obtain the precise limiting variance of the estimator in terms of these parame...
• STRUCTURAL RESULTS FOR THE TREE BUILDER RANDOM WALK AI翻译
  作者：Englander, Janos; Iacobelli, Giulio; Pete, Gabor; Ribeiro, Rodrigo
  作者单位：University of Colorado System; University of Colorado Boulder; Universidade Federal do Rio de Janeiro; HUN-REN; HUN-REN Alfred Renyi Institute of Mathematics; Budapest University of Technology & Economics; University of Denver
  摘要：We study the tree builder random walk: a randomly growing tree, built by a walker as she is walking around the tree. Namely, at each time n , she adds a leaf to her current vertex with probability pn = n-gamma , gamma is an element of ( 2 / 3 , 1], then moves to a uniform random neighbor on the possibly modified tree. We show that the tree process at its growth times, after a random finite number of steps, can be coupled to be identical to the Barab & aacute;si-Albert preferential attachment t...
• INSIGHT FROM THE KULLBACK-LEIBLER DIVERGENCE INTO ADAPTIVE IMPORTANCE SAMPLING SCHEMES FOR RARE EVENT ANALYSIS IN HIGH DIMENSION AI翻译
  作者：Beh, Jason; Shadmi, Yonatan; Simatos, Florian
  作者单位：Universite de Toulouse; National Office for Aerospace Studies & Research (ONERA); Technion Israel Institute of Technology; Universite de Toulouse; Institut Superieur de l'Aeronautique et de l'Espace (ISAE-SUPAERO); National Office for Aerospace Studies & Research (ONERA)
  摘要：We study two adaptive importance sampling schemes for estimating the probability of a rare event in the high-dimensional regime d - oc with d the dimension. The first scheme is the prominent cross-entropy (CE) method, and the second scheme, motivated by recent results, uses as auxiliary distribution a projection of the optimal auxiliary distribution on a lower-dimensional subspace. In these schemes, two samples are used: the first one to learn the auxiliary distribution and the second one, dra...
• CONVERGENCE OF DIRICHLET FORMS FOR MCMC OPTIMAL SCALING WITH DEPENDENT TARGET DISTRIBUTIONS ON LARGE GRAPHS AI翻译
  作者：Ning, Ning
  作者单位：Texas A&M University System; Texas A&M University College Station
  摘要：Markov chain Monte Carlo (MCMC) algorithms have played a significant role in statistics, physics, machine learning and others, and they are the only known general and efficient approach for some high-dimensional problems. The random walk Metropolis (RWM) algorithm as the most classical MCMC algorithm, has had a great influence on the development and practice of science and engineering. The behavior of the RWM algorithm in high-dimensional problems is typically investigated through a weak conve...
• THE ODE METHOD FOR ASYMPTOTIC STATISTICS IN STOCHASTIC APPROXIMATION AND REINFORCEMENT LEARNING AI翻译
  作者：Borkar, Vivek; Chen, Shuhang; Devraj, Adithya; Kontoyiannis, Ioannis; Meyn, Sean
  作者单位：Indian Institute of Technology System (IIT System); Indian Institute of Technology (IIT) - Bombay; State University System of Florida; University of Florida; Stanford University; University of Cambridge; State University System of Florida; University of Florida
  摘要：The paper concerns the stochastic approximation recursion, theta n+1 = theta n + alpha n+1f (theta n, Phi n+1), n >= 0, where the estimates {theta n} evolve on Ilgd, and Phi := {Phi n} is a stochastic process on a general state space, satisfying a conditional Markov property that allows for parameter-dependent noise. In addition to standard Lipschitz assumptions and conditions on the vanishing step-size sequence, it is assumed that the associated mean flow ddt theta t =f(theta t) is globally a...
• CUTOFF PHENOMENON IN NONLINEAR RECOMBINATIONS AI翻译
  作者：Caputo, Pietro; Labbe, Cyril; Lacoin, Hubert
  作者单位：Roma Tre University; Universite Paris Cite; Instituto Nacional de Matematica Pura e Aplicada (IMPA)
  摘要：We investigate a quadratic dynamical system known as nonlinear recombinations. This system models the evolution of a probability measure over the Boolean cube, converging to the stationary state obtained as the product of the initial marginals. Our main result reveals a cutoff phenomenon for the total variation distance in both discrete and continuous time. Additionally, we derive the explicit cutoff profiles in the case of monochromatic initial distributions. These profiles are different in t...