Comparison theorem and estimates for transition probability densities of diffusion processes
type: Item
instance of: scholarly article
title: Comparison theorem and estimates for transition probability densities of diffusion processes
zbMATH Open document ID: 1050.60061
author: Zhongmin Qian
author: Francesco Russo
author: Weian Zheng
publication date: 2004-03-11T00:00:00Z
review text: Consider the solution to an \(n\)-dimensional stochastic differential equation with drift coefficient \(b(x)\) and constant diffusion coefficient given by the identity (called Brownian motion with drift \(b\) by the authors). For such processes several comparison theorems for the transition probability density \(p_b(x,t,y)\) are established. Sharp lower and upper bounds in terms of the norm on the vector field \(b\) with explicitly given constants are established. \(b\) is neither assumed to be symmetrical nor to be the gradient of a function. The main result is obtained through comparison with a Bessel process with constant drift. In order to do this, estimates for some mixed moments of the Bessel process are derived.
reviewed by: Bo Markussen
Mathematics Subject Classification ID: 60H10
Mathematics Subject Classification ID: 60H30
Mathematics Subject Classification ID: 60J35
Mathematics Subject Classification ID: 35K05
zbMATH DE Number: 2055259
zbMATH Keywords: transition probabilities
zbMATH Keywords: diffusion processes
zbMATH Keywords: comparison theorems
zbMATH Keywords: Bessel processes
MaRDI profile type: Publication
full work available at URL: s00440-003-0291-1
OpenAlex ID: W2038911169
DOI: 10.1007/S00440-003-0291-1
published in: Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete
description: scientific article; zbMATH DE number 2055259