Sharp bounds on the density, Green function and jumping function of subordinate killed BM
type: Item
instance of: scholarly article
title: Sharp bounds on the density, Green function and jumping function of subordinate killed BM
zbMATH Open document ID: 1054.60080
author: Renming Song
publication date: 2004-07-01T00:00:00Z
review text: Let \(D\subset \mathbb{R}^d\) be a \(C^{1,1}\)- or an exterior \(C^{1,1}\)-domain. On \(D\) consider the Laplacian \(\Delta_D\) with Dirichlet boundary data. Use an \(\alpha/2\)-stable subordinator to define a Markov jump process \((Z_t)_{t>0}\) with generator \(-(-\Delta_D)^{\alpha/2}\). The author proves sharp upper and lower bounds to the densities of the Green's and the transition function of \((Z_t)_t\). Here ``sharp'' means that the upper and lower bounds only differ by a multiplicative constant. When the classical Brownian motion is first subordinated and then killed, the result is of course different from \((Z_t)_t\).
reviewed by: Volker Metz
Mathematics Subject Classification ID: 60J35
Mathematics Subject Classification ID: 31B05
zbMATH DE Number: 2077981
zbMATH Keywords: Brownian motion
zbMATH Keywords: killing
zbMATH Keywords: subordination
MaRDI profile type: Publication
published in: Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete
description: scientific article; zbMATH DE number 2077981