Interacting Brownian motions with measurable potentials
type: Item
instance of: scholarly article
title: Interacting Brownian motions with measurable potentials
zbMATH Open document ID: 0909.60066
author: Hirofumi Osada
published in: Proceedings of the Japan Academy. Series A
publication date: 1999-03-21T00:00:00Z
review text: The author considers the infinitely dimensional diffusion process \[ dX^i_t = d B^i_t - \sum_{j=1, j\neq i}^{\infty} \tfrac{1}{2}\bigtriangledown \Phi (X_t^i - X_t^i) dt, \;\;1\leq i \leq {+\infty}, \] where the measurable function \(\Phi \) is the interacting potential, which is dominated by a function with some regularity properties. On the set of all locally finite configurations on \({\mathbb R^d}\), denoted by \(\Theta\), a Dirichlet form \(E\) and the set \(D\) of functions of \(L^2(\Theta, \mu)\) for which the Dirichlet form is finite, are considered, where \(\mu\) is a canonical (Gibbs) measure associated with \(\Phi\). The main result states that \((E, D)\) is closable on \(L^2(\Theta,\mu)\).
Mathematics Subject Classification ID: 60J65
zbMATH DE Number: 1192510
zbMATH Keywords: diffusion process
zbMATH Keywords: interacting potential
zbMATH Keywords: Dirichlet form
reviewed by: Liliana Popa
MaRDI profile type: Publication
full work available at URL: pjaa.74.10
OpenAlex ID: W2092080739
DOI: 10.3792/PJAA.74.10
description: scientific article; zbMATH DE number 1192510