Spectral properties for a class of continuous state branching processes with immigration.
type: Item
instance of: scholarly article
title: Spectral properties for a class of continuous state branching processes with immigration.
zbMATH Open document ID: 1039.60076
DOI: 10.1016/S0022-1236(03)00088-0
author: Wilhelm Stannat
published in: Journal of Functional Analysis
publication date: 2003-08-25T00:00:00Z
review text: The paper is a part of general program which consists in finding nontrivial classes of measure-valued processes with a good \(L^{2}\) [see also the author, Ann. Probab. 28, No. 2, 667-684 (2000; Zbl 1044.60037), Probab. Theory Relat. Fields 122, No. 3, 431-469 (2002; Zbl 1001.60079) and Ann. Probab. 31, No. 3, 1377--1412 (2003; Zbl 1043.60076)]. In the present paper the author constructs non-trivial invariant measures (including Gamma measure or path space measures of Lévy subordinators) for a class of continuous state branching processes with immigration. Long time behaviour and hypercontractivity of the transition semigroups are studied.
Mathematics Subject Classification ID: 60J80
Mathematics Subject Classification ID: 60G57
zbMATH DE Number: 1970668
zbMATH Keywords: superprocesses with immigration
zbMATH Keywords: invariant measures
zbMATH Keywords: hypercontractivity
reviewed by: Mihai Gradinaru
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1970668