Geodesic
Spatial Branching Processes and Subordination
Canadian journal of mathematics, Tome 49 (1997) no. 1, pp. 24-54

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

We present a subordination theory for spatial branching processes. This theory is developed in three different settings, first for branching Markov processes, then for superprocesses and finally for the path-valued process called the Brownian snake. As a common feature of these three situations, subordination can be used to generate new branching mechanisms. As an application, we investigate the compact support property for superprocesses with a general branching mechanism.
DOI : 10.4153/CJM-1997-002-x
Mots-clés : 60J80, 60J25, 60J27, 60J55, 60G57 
Bertoin, Jean; Gall, Jean-François Le; Jan, Yves Le. Spatial Branching Processes and Subordination. Canadian journal of mathematics, Tome 49 (1997) no. 1, pp. 24-54. doi: 10.4153/CJM-1997-002-x
@article{10_4153_CJM_1997_002_x,
     author = {Bertoin, Jean and Gall, Jean-Fran\c{c}ois Le and Jan, Yves Le},
     title = {Spatial {Branching} {Processes} and {Subordination}},
     journal = {Canadian journal of mathematics},
     pages = {24--54},
     year = {1997},
     volume = {49},
     number = {1},
     doi = {10.4153/CJM-1997-002-x},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1997-002-x/}
}
TY  - JOUR
AU  - Bertoin, Jean
AU  - Gall, Jean-François Le
AU  - Jan, Yves Le
TI  - Spatial Branching Processes and Subordination
JO  - Canadian journal of mathematics
PY  - 1997
SP  - 24
EP  - 54
VL  - 49
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-1997-002-x/
DO  - 10.4153/CJM-1997-002-x
ID  - 10_4153_CJM_1997_002_x
ER  - 
%0 Journal Article
%A Bertoin, Jean
%A Gall, Jean-François Le
%A Jan, Yves Le
%T Spatial Branching Processes and Subordination
%J Canadian journal of mathematics
%D 1997
%P 24-54
%V 49
%N 1
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-1997-002-x/
%R 10.4153/CJM-1997-002-x
%F 10_4153_CJM_1997_002_x

[1] 1. Bertoin, J., Lévy Processes, Cambridge Univ. Press, 1996. Google Scholar

[2] 2. Billingsley, P., Convergence of Probability Measures, Wiley, New York, 1968. Google Scholar

[3] 3. Chauvin, B., Product martingales and stopping lines for branching Brownian motion, Ann. Probab. 19(1991), 1195.ndash;1205. Google Scholar

[4] 4. Dawson, D.A., Iscoe, I. and Perkins, E.A., Super-Brownian motion: Path properties and hitting probabilities, Probab. Theor. Relat. Field. 83(1989), 135–205. Google Scholar

[5] 5. Dawson, D.A. and Perkins, E.A., Historical processes, ,Mem. Amer.Math. Soc.. 454(1991). Google Scholar

[6] 6. Dawson, D.A. and Vinogradov, V., Almost sure path properties of(2Ò dÒ å) superprocesses, Stochastic Process. Appl. 51(1994), 221–258. Google Scholar

[7] 7. Dellacherie, C., Maisonneuve, B. and Meyer, P.A., Probabilités et Potentiel, Processus de Markov (fin), Compléments de Calcul Stochastique, Hermann, Paris, 1992. Google Scholar

[8] 8. Delmas, J.F., Path properties of superprocesses with a general branching mechanism, preprint, 1996. Google Scholar

[9] 9. Dynkin, E.B., Branching particle systems and superprocesses, Ann. Probab. 19(1991), 1157.ndash;1194. Google Scholar

[10] 10. Dynkin, E.B. , A probabilistic approach to one class of nonlinear differential equations, Probab. Theor. Relat. Field. 89(1991), 89–115. Google Scholar

[11] 11. Dynkin, E.B., Superdiffusions and parabolic nonlinear differential equations, Ann. Probab. 20(1992), 942– 962. Google Scholar

[12] 12. Dynkin, E.B. , Superprocesses and partial differential equations, Ann. Probab. 21(1993), 1185.ndash;1262. Google Scholar

[13] 13. Dynkin, E.B. and Kuznetsov, S.E., Markov snakes and superprocesses, Probab. Theor. Relat. Field. 103(1995), 433-473. Google Scholar

[14] 14. El Karoui, N. and Roelly, S., Propriétés de martingales, explosion et représentation de Lévy-Khintchine d’une classe de processus de branchement à valeurs mesures, Stochastic Process. Appl. 38(1991), 239–266. Google Scholar

[15] 15. Gnedenko, B.V. and Kolmogorov, A.N., Limit Distributions for Sums of Independent Random Variables, Addison-Wesley, Cambridge, 1954. Google Scholar

[16] 16. Kaj, I. and Salminen, P., On a first passage problem for branching Brownian motions, Ann. Appl. Probab. 3(1993), 173–185. Google Scholar

[17] 17. Le Gall, J.F., A class of path-valued Markov processes and its applications to superprocesses, Probab. Theor. Relat. Field. 95(1993), 25–46. Google Scholar

[18] 18. Le Gall, J.F., A path-valued Markov process and its connections with partial differential equations, Proc. 1st European Congress of Math., Vol. II, 185–212, Birkhäuser, Boston, 1994. Google Scholar

[19] 19. Le Gall, J.F., The Brownian snake and solutions ofΔu= u2 in a domain, Probab. Theor. Relat. Field. 102(1995), 393–432. Google Scholar

[20] 20. Le Gall, J.F. , Brownian snakes, superprocesses and partial differential equations, in preparation. Google Scholar

[21] 21. Le Gall, J.F. and Perkins, E.A., TheHausdorff measure of the support of two-dimensional super-Brownian motion, Ann. Probab. 23(1995), 1719.1747. Google Scholar

[22] 22. Neveu, J., Vers un problème de Dirichlet pour le processus de branchement brownien, unpublished lecture, Université Paris VI, 1988. Google Scholar

[23] 23. Watanabe, S., A limit theorem of branching processes and continuous state branching processes, J.Math. Kyoto Univ. 8(1968), 141–167. Google Scholar

Cité par Sources :