Joint continuity of the intersection local times of Markov processes
type: Item
instance of: scholarly article
title: Joint continuity of the intersection local times of Markov processes
zbMATH Open document ID: 0622.60084
published in: The Annals of Probability
publication date: 1987-01-01T00:00:00Z
review text: This paper gives simple conditions on the transition densities of two independent Markov processes X and Y in \({\mathbb{R}}^ d\), which guarantee the existence of the intersection local time of X and Y, i.e. of a continuous density for the measure: \[ f\to \iint_{H}f(X_ s-Y_ t)ds dt, \] where H is any bounded Borel subset of \(({\mathbb{R}}_+)^ 2\). These conditions are satisfied in the case of smooth elliptic diffusions in \({\mathbb{R}}^ d\), for \(d=2\) or 3. Under similar assumptions, the author also proves the existence of a local time of self-intersections for the single process X, continuous except at \(x=0\). In the case of smooth elliptic diffusions, he establishes a Tanaka-like formula for this local time, which in the two-dimensional case can be used to study the singularity at \(x=0\).
Mathematics Subject Classification ID: 60J60
Mathematics Subject Classification ID: 60J55
Mathematics Subject Classification ID: 60J25
zbMATH DE Number: 4009481
zbMATH Keywords: renormalization
zbMATH Keywords: existence of the intersection local time
zbMATH Keywords: self- intersections
zbMATH Keywords: Tanaka-like formula
author: Jay Rosen
reviewed by: J.-F. Le Gall
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aop/1176992164
OpenAlex ID: W2044600157
DOI: 10.1214/AOP/1176992164
description: scientific article; zbMATH DE number 4009481