Hostname: page-component-586b7cd67f-rdxmf Total loading time: 0 Render date: 2024-11-28T03:42:54.993Z Has data issue: false hasContentIssue false
  • English
  • Français

A proof of the persistence criterion for a class of superprocesses

Part of: Markov processes Stochastic processes

Published online by Cambridge University Press:  14 July 2016

Yong-Jin Wang
Yong-Jin Wang*
Affiliation:
Nankai University
*
∗Postal address: Department of Mathematics, Nankai University, Tianjin, 300071, China.
Get access Rights & Permissions [Opens in a new window]

Abstract

Gorostiza and Wakolbinger (1991), and Dawson and Perkins (1991) established the same persistence criterion for a class of critical branching particle systems and for a class of superprocesses respectively. In this note we take another approach to the criterion and present a simpler proof of it.

Keywords

SUPERPROCESSPERSISTENCESYMMETRIC STABLE PROCESSES

MSC classification

Primary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.) 60G57: Random measures
Type
Short Communications
Information
Journal of Applied Probability , Volume 34 , Issue 2 , June 1997 , pp. 559 - 563
Copyright
Copyright © Applied Probability Trust 1997 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Dawson, D. A. (1993) Measure-valued Markov Processes. (Lecture Notes in Mathematics 1541.) Springer, Berlin.CrossRefGoogle Scholar
Dawson, D. A., Fleischmann, K., Foley, R. D. and Peletier, L. A. (1986) A critical measure-valued branching process with infinite mean. Stoch. Anal. Appl. 4, 117–129.Google Scholar
Dawson, D. A. and Perkins, E. A. (1991) Historical processes. Mem. Amer. Math. Soc. 93, 454.Google Scholar
Gorostiza, L. G., Roelly-Coppoletta, S. and Wakolbinger, A. (1990) Sur la persistance du processus de Dawson-Watanabe stable. L'interversion de la limite en temps et de la renormalisation. Sém. Prob. XXIV (Lecture Notes in Mathematics 1426.) Springer, Berlin, pp 275–281.Google Scholar
Gorostiza, L. G. and Wakolbinger, A. (1991) Persistence criteria for a class of critical branching particle systems in continuous time. Ann. Prob. 19, 266–288.CrossRefGoogle Scholar
Iscoe, I. (1986) A weighted occupation time for a class of measure-valued branching process. Prob. Theory Rel. Fields 71, 85–116.Google Scholar