Transition density estimates for stable processes on symmetric spaces
type: Item
instance of: scholarly article
title: Transition density estimates for stable processes on symmetric spaces
zbMATH Open document ID: 1067.60017
author: Piotr Graczyk
author: Andrzej Stós
published in: Pacific Journal of Mathematics
publication date: 2005-05-03T00:00:00Z
review text: The authors obtain exact upper and lower estimates for transition densities of \(\alpha\)-stable processes on Riemannian symmetric spaces of noncompact type. These processes are defined by a subordination procedure [\textit{R. K. Getoor}, Pac. J. Math. 11, 1287--1308 (1961; Zbl 0124.34502)], and their scaling properties were not known. The above estimates possess certain scaling properties, which can be interpreted as weak scaling properties of the processes themselves. Earlier, some estimates for the above transition densities were found for \(\alpha =1\) [\textit{J.-P. Anker} and \textit{L. Ji}, Geom. Funct. Anal. 9, No. 6, 1035--1091 (1999; Zbl 0942.43005)]; large time estimates were known in the rank one case [\textit{J.-C. Gruet}, Ann. Math. Blaise Pascal 5, No. 2, 39--48 (1998; Zbl 0926.60020)].
reviewed by: Anatoly N. Kochubei
Mathematics Subject Classification ID: 60G52
Mathematics Subject Classification ID: 43A85
Mathematics Subject Classification ID: 60B15
Mathematics Subject Classification ID: 60J35
zbMATH DE Number: 2164608
zbMATH Keywords: subordination
MaRDI profile type: Publication
full work available at URL: pjm.2004.217.87
OpenAlex ID: W1968562805
DOI: 10.2140/PJM.2004.217.87
description: scientific article; zbMATH DE number 2164608