Two-sided heat kernel estimates for censored stable-like processes
type: Item
instance of: scholarly article
title: Two-sided heat kernel estimates for censored stable-like processes
zbMATH Open document ID: 1190.60068
author: Zhen-Qing Chen
author: Panki Kim
author: Renming Song
publication date: 2010-02-09T00:00:00Z
review text: Let \(D\subset \mathbb R^d\) be an open subset. A censored \(\alpha\)-stable-like process in \(D\) is a strong Markov process whose infinitesimal generator is given by \[ (L_D^\alpha u)(x)=\lim_{\varepsilon \to 0}\int_{y\in D:\;|y-x|>\varepsilon}(u(y)-u(x))\frac{C(x,y)}{|x-y|^{d+\alpha }}\,dy,\quad u\in C_0^2(D), \] where \(C(x,y)\) is a measurable symmetric function on \(D\times D\), \(0<C_1\leq C(x,y)\leq C_2<\infty\). Under various assumptions, the authors find sharp two-sided estimates for the transition densities and Green functions of such processes.
Mathematics Subject Classification ID: 60J35
Mathematics Subject Classification ID: 47D07
Mathematics Subject Classification ID: 60J75
zbMATH DE Number: 5668288
zbMATH Keywords: censored stable-like process
zbMATH Keywords: transition density
zbMATH Keywords: Green function
reviewed by: Anatoly N. Kochubei
MaRDI profile type: Publication
full work available at URL: s00440-008-0193-3
OpenAlex ID: W2139112237
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DOI: 10.1007/S00440-008-0193-3
published in: Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete
description: scientific article; zbMATH DE number 5668288