Periodic homogenization for hypoelliptic diffusions
type: Item
instance of: scholarly article
title: Periodic homogenization for hypoelliptic diffusions
zbMATH Open document ID: 1130.82026
DOI: 10.1023/B:JOSS.0000044055.59822.20
author: Yanyan Li
published in: Journal of Statistical Physics
publication date: 2006-10-11T00:00:00Z
full work available at URL: https://arxiv.org/abs/math-ph/0403003
review text: The long time behavior of an Ornstein-Uhlenbeck process is investigated, under the influence of a periodic drift. That involves the problem of homogenization for periodic hypoelliptic diffusions. It is proved that the rescaled particle position weakly converges to a Brownian motion, whose covariance matrix is determined by a solution of the Poisson equation. Estimates on the particle velocity are established. Upper bounds on the convergence rate in several norms were obtained and an optimality of the \(p\)-Wassserstein metric was indicated.
reviewed by: Piotr Garbaczewski
Mathematics Subject Classification ID: 82C31
Mathematics Subject Classification ID: 60G35
Mathematics Subject Classification ID: 60F05
zbMATH DE Number: 5062501
zbMATH Keywords: Diffusion processes
zbMATH Keywords: Ornstein-Uhlenbeck process
zbMATH Keywords: Langevin equation
zbMATH Keywords: Smoluchowski equation
zbMATH Keywords: martingale central limit theorem
zbMATH Keywords: hypoellipticity
zbMATH Keywords: periodic homogeneization
zbMATH Keywords: Poisson equation
MaRDI profile type: Publication
arXiv ID: math-ph/0403003
OpenAlex ID: W1964981294
description: scientific article