Hostname: page-component-586b7cd67f-rdxmf Total loading time: 0 Render date: 2024-11-22T04:17:29.548Z Has data issue: false hasContentIssue false
  • English
  • Français

The Entrance Space of a Measure-Valued Markov Branching Process Conditioned on Non-Extinction

Published online by Cambridge University Press:  20 November 2018

Steven N. Evans
Steven N. Evans*
Affiliation:
Department of Statistics University of California 367 Evans Hall Berkeley, CA 94720 USA
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We explicitly identify the possible probability entrance laws for a class of measure-valued processes that are constructed by taking a particular measure-valued Markov branching process and conditioning it to stay away from the zero measure trap. The set of extreme points of the entrance space is larger than the state space of the conditioned process, and contains elements which correspond to starting the conditioned process at the zero measure.

Keywords

60J5060G5760J2560J80.branching processmeasure-valuedentrance spaceentrance law.
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 35 , Issue 1 , 01 March 1992 , pp. 70 - 74
Copyright
Copyright © Canadian Mathematical Society 1992

References

1. Dynkin, E. B. (1988), Representation offunctional of superprocesses by multiple stochastic integrals, with applications to self-intersection local times. In Colloque Paul Levy sur les processus stochastiques, Astérisque, Société Mathématique de France, 1988,157-158.Google Scholar
2. Dynkin, E. B., (1989), Regular transition functions and regular superprocesses, Trans. Amer. Math. Soc, 316 (1989), 623–634.Google Scholar
3. El Karoui, N. and Roelly-Coppoletta, S. (1987), Study of a general class of measure-valued branching processes; a Lévy-Hincin representation. Preprint.Google Scholar
4. Ethier, S. N. and Kurtz, T. G. (1986), Markov processes: characterization and convergence. Wiley, 1986.Google Scholar
5. Evans, S. N. and E. Perkins (1990), Measure-valued Markov branching processes conditioned on nonextinction, Israel J. Math., 71(1990),329–337.Google Scholar
6. Feller, W. (1951), Diffusion processes in genetics. Proc. Second Berkeley Symp. Math. Statist. Prob., University of California Press, 1951, 227–246.Google Scholar
7. Fitzsimmons, P. J. (1988), Construction and regularity of measure-valued Markov branching processes, Israel J. Math. 64(1988),337–361.Google Scholar
8. Kallenberg, O. (1983), Random measures. (3rd edition) Akademie-Verlag, Academic Press, 1983.Google Scholar
9. Knight, F. B. (1981), Essentials of Brownian Motion and Diffusion. Mathematical Surveys Number 18, American Mathematical Society, 1981.Google Scholar
10. Pitman, J. and Yor, M. (1982), A decomposition of Bessel bridges, Z. Wahrscheinlichkeitstheorie verw. Gebiete 59(1982), 425–457.Google Scholar
11. S. Roelly-Coppoletta and Rouault, A. (1989), Processus de Dawson-Watanabe conditionné par le futur lointain, C.R. Acad. Sci. Paris 309, Série I (1989), 867–872.Google Scholar
12. Sharpe, M. J. (1988), General theory of Markov processes. Academic Press, 1988. Google Scholar
13. Watanabe, S. (1968), A limit theorem of branching processes and continuous state branching processes, J. Math. Kyoto Univ. 8(1968),141–167.Google Scholar