Geodesic
The Entrance Space of a Measure-Valued Markov Branching Process Conditioned on Non-Extinction
Canadian mathematical bulletin, Tome 35 (1992) no. 1, pp. 70-74

Voir la notice de l'article provenant de la source Cambridge University Press

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.
DOI : 10.4153/CMB-1992-010-8
Mots-clés : 60J50, 60G57, 60J25, 60J80., branching process, measure-valued, entrance space, entrance law. 
Evans, Steven N. The Entrance Space of a Measure-Valued Markov Branching Process Conditioned on Non-Extinction. Canadian mathematical bulletin, Tome 35 (1992) no. 1, pp. 70-74. doi: 10.4153/CMB-1992-010-8
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[1] 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] 2. Dynkin, E. B., (1989), Regular transition functions and regular superprocesses, Trans. Amer. Math. Soc, 316 (1989), 623–634. Google Scholar

[3] 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] 4. Ethier, S. N. and Kurtz, T. G. (1986), Markov processes: characterization and convergence. Wiley, 1986. Google Scholar

[5] 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] 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] 7. Fitzsimmons, P. J. (1988), Construction and regularity of measure-valued Markov branching processes, Israel J. Math. 64(1988),337–361. Google Scholar

[8] 8. Kallenberg, O. (1983), Random measures. (3rd edition) Akademie-Verlag, Academic Press, 1983. Google Scholar

[9] 9. Knight, F. B. (1981), Essentials of Brownian Motion and Diffusion. Mathematical Surveys Number 18, American Mathematical Society, 1981. Google Scholar

[10] 10. Pitman, J. and Yor, M. (1982), A decomposition of Bessel bridges, Z. Wahrscheinlichkeitstheorie verw. Gebiete 59(1982), 425–457. Google Scholar

[11] 11. S. Roelly-Coppoletta and Rouault, A. (1989), Processus de Dawson-Watanabe conditionné par le futur lointain, C.R. Acad. Sci. Paris , Série I (1989), 867–872. Google Scholar

[12] 12. Sharpe, M. J. (1988), General theory of Markov processes. Academic Press, 1988. Google Scholar

[13] 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

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