4期

最新文章

• MIXING TIME AND CUTOFF FOR THE WEAKLY ASYMMETRIC SIMPLE EXCLUSION PROCESS AI翻译
  作者：Labbe, Cyril; Lacoin, Hubert
  作者单位：Universite PSL; Universite Paris-Dauphine
  摘要：We consider the simple exclusion process with k particles on a segment of length N performing random walks with transition p > 1/2 to the right and q = 1 - p to the left. We focus on the case where the asymmetry in the jump rates b = p - q > 0 vanishes in the limit when N and k tend to infinity, and obtain sharp asymptotics for the mixing times of this sequence of Markov chains in the two cases where the asymmetry is either much larger or much smaller than (log k)/N. We show that in the former...
• SENSITIVITY ANALYSIS FOR RARE EVENTS BASED ON RENYI DIVERGENCE AI翻译
  作者：Dupuis, Paul; Katsoulakis, Markos A.; Pantazis, Yannis; Rey-Bellet, Luc
  作者单位：Brown University; University of Massachusetts System; University of Massachusetts Amherst; Foundation for Research & Technology - Hellas (FORTH)
  摘要：Rare events play a key role in many applications and numerous algorithms have been proposed for estimating the probability of a rare event. However, relatively little is known on how to quantify the sensitivity of the rare event's probability with respect to model parameters. In this paper, instead of the direct statistical estimation of rare event sensitivities, we develop novel and general uncertainty quantification and sensitivity bounds which are not tied to specific rare event simulation ...
• HYDRODYNAMIC LIMIT AND PROPAGATION OF CHAOS FOR BROWNIAN PARTICLES REFLECTING FROM A NEWTONIAN BARRIER AI翻译
  作者：Barnes, Clayton L.
  作者单位：Technion Israel Institute of Technology
  摘要：In 2001, Frank Knight constructed a stochastic process modeling the one-dimensional interaction of two particles, one being Newtonian in the sense that it obeys Newton's laws of motion, and the other particle being Brownian. We construct a multi-particle analog, using Skorohod map estimates in proving a propagation of chaos, and characterizing the hydrodynamic limit as the solution to a PDE with free boundary condition. This PDE resembles the Stefan problem but has a Neumann type boundary cond...
• EDGEWORTH EXPANSION FOR EULER APPROXIMATION OF CONTINUOUS DIFFUSION PROCESSES AI翻译
  作者：Podolskij, Mark; Veliyev, Bezirgen; Yoshida, Nakahiro
  作者单位：Aarhus University; CREATES; Aarhus University; University of Tokyo
  摘要：In this paper we present the Edgeworth expansion for the Euler approximation scheme of a continuous diffusion process driven by a Brownian motion. Our methodology is based upon a recent work (Stochastic Process. Appl. 123 (2013) 887-933), which establishes Edgeworth expansions associated with asymptotic mixed normality using elements of Malliavin calculus. Potential applications of our theoretical results include higher order expansions for weak and strong approximation errors associated to th...
• RANDOM WALK ON RANDOM WALKS: LOW DENSITIES AI翻译
  作者：Blondel, Oriane; Hilario, Marcelo R.; dos Santos, Renato S.; Sidoravicius, Vladas; Teixeira, Augusto
  作者单位：Universite Claude Bernard Lyon 1; Centre National de la Recherche Scientifique (CNRS); Universidade Federal de Minas Gerais; New York University; NYU Shanghai
  摘要：We consider a random walker in a dynamic random environment given by a system of independent discrete-time simple symmetric random walks. We obtain ballisticity results under two types of perturbations: low particle density, and strong local drift on particles. Surprisingly, the random walker may behave very differently depending on whether the underlying environment particles perform lazy or nonlazy random walks, which is related to a notion of permeability of the system. We also provide a st...
• ON BAYESIAN CONSISTENCY FOR FLOWS OBSERVED THROUGH A PASSIVE SCALAR AI翻译
  作者：Borggaard, Jeff; Glatt-Holtz, Nathan; Krometis, Justin
  作者单位：Virginia Polytechnic Institute & State University; Tulane University; Virginia Polytechnic Institute & State University
  摘要：We consider the statistical inverse problem of estimating a background fluid flow field v from the partial, noisy observations of the concentration theta of a substance passively advected by the fluid, so that theta is governed by the partial differential equation partial derivative/partial derivative(t )theta (t, x) = - v(x) . del theta(t, x) + kappa Delta theta(t, x), theta(0, x) =theta(0)(x) for t is an element of [0, T], T > 0 and x is an element of T-2 = [0, 1](2). The initial condition t...
• APPROXIMATION SCHEMES FOR VISCOSITY SOLUTIONS OF FULLY NONLINEAR STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS AI翻译
  作者：Seeger, Benjamin
  作者单位：Universite PSL; Universite Paris-Dauphine; Universite PSL; College de France
  摘要：The aim of this paper is to develop a general method for constructing approximation schemes for viscosity solutions of fully nonlinear pathwise stochastic partial differential equations, and for proving their convergence. Our results apply to approximations such as explicit finite difference schemes and Trotter-Kato type mixing formulas. The irregular time dependence disrupts the usual methods from the classical viscosity theory for creating schemes that are both monotone and convergent, an ob...
• NONASYMPTOTIC BOUNDS FOR SAMPLING ALGORITHMS WITHOUT LOG-CONCAVITY AI翻译
  作者：Majka, Mateusz B.; Mijatovic, Aleksandar; Szpruch, Lukasz
  作者单位：University of Warwick; Alan Turing Institute; University of Edinburgh
  摘要：Discrete time analogues of ergodic stochastic differential equations (SDEs) are one of the most popular and flexible tools for sampling high-dimensional probability measures. Non-asymptotic analysis in the L-2 Wasserstein distance of sampling algorithms based on Euler discretisations of SDEs has been recently developed by several authors for log-concave probability distributions. In this work we replace the log-concavity assumption with a log-concavity at infinity condition. We provide novel L...
• ON THE CONVERGENCE OF CLOSED-LOOP NASH EQUILIBRIA TO THE MEAN FIELD GAME LIMIT AI翻译
  作者：Lacker, Daniel
  作者单位：Columbia University
  摘要：This paper continues the study of the mean field game (MFG) conver- gence problem: In what sense do the Nash equilibria of n-player stochastic differential games converge to the mean field game as n -> infinity? Previous work on this problem took two forms. First, when the n-player equilibria are openloop, compactness arguments permit a characterization of all limit points of n-player equilibria as weak MFG equilibria, which contain additional randomness compared to the standard (strong) equil...
• HIGH-DIMENSIONAL LIMITS OF EIGENVALUE DISTRIBUTIONS FOR GENERAL WISHART PROCESS AI翻译
  作者：Song, Jian; Yao, Jianfeng; Yuan, Wangjun
  作者单位：Shandong University; University of Hong Kong; University of Hong Kong
  摘要：In this article, we obtain an equation for the high-dimensional limit measure of eigenvalues of generalized Wishart processes, and the results are extended to random particle systems that generalize SDEs of eigenvalues. We also introduce a new set of conditions on the coefficient matrices for the existence and uniqueness of a strong solution for the SDEs of eigenvalues. The equation of the limit measure is further discussed assuming self-similarity on the eigenvalues.