The Martin entrance boundary of the Galton-Watson process

Alsmeyer, Gerold; Rösler, Uwe

doi:10.1016/j.anihpb.2005.05.003

Alsmeyer, Gerold ; Rösler, Uwe

Annales de l'I.H.P. Probabilités et statistiques, Tome 42 (2006) no. 5, pp. 591-606.

Zbl

DOI : 10.1016/j.anihpb.2005.05.003

@article{AIHPB_2006__42_5_591_0,
     author = {Alsmeyer, Gerold and R\"osler, Uwe},
     title = {The {Martin} entrance boundary of the {Galton-Watson} process},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     pages = {591--606},
     publisher = {Elsevier},
     volume = {42},
     number = {5},
     year = {2006},
     doi = {10.1016/j.anihpb.2005.05.003},
     zbl = {05068238},
     language = {en},
     url = {http://www.numdam.org/articles/10.1016/j.anihpb.2005.05.003/}
}

TY  - JOUR
AU  - Alsmeyer, Gerold
AU  - Rösler, Uwe
TI  - The Martin entrance boundary of the Galton-Watson process
JO  - Annales de l'I.H.P. Probabilités et statistiques
PY  - 2006
SP  - 591
EP  - 606
VL  - 42
IS  - 5
PB  - Elsevier
UR  - http://www.numdam.org/articles/10.1016/j.anihpb.2005.05.003/
DO  - 10.1016/j.anihpb.2005.05.003
LA  - en
ID  - AIHPB_2006__42_5_591_0
ER  -

%0 Journal Article
%A Alsmeyer, Gerold
%A Rösler, Uwe
%T The Martin entrance boundary of the Galton-Watson process
%J Annales de l'I.H.P. Probabilités et statistiques
%D 2006
%P 591-606
%V 42
%N 5
%I Elsevier
%U http://www.numdam.org/articles/10.1016/j.anihpb.2005.05.003/
%R 10.1016/j.anihpb.2005.05.003
%G en
%F AIHPB_2006__42_5_591_0

Alsmeyer, Gerold; Rösler, Uwe. The Martin entrance boundary of the Galton-Watson process. Annales de l'I.H.P. Probabilités et statistiques, Tome 42 (2006) no. 5, pp. 591-606. doi : 10.1016/j.anihpb.2005.05.003. http://www.numdam.org/articles/10.1016/j.anihpb.2005.05.003/

Bibliographie
Cité par

[1] G. Alsmeyer, U. Rösler, Asexual versus promiscuous bisexual Galton-Watson processes: The extinction probability ratio, Ann. Appl. Probab. 12 (2002) 125-142. | MR | Zbl

[2] S. Asmussen, H. Hering, Branching Processes, Birkhäuser, Boston, 1983. | MR | Zbl

[3] K.B. Athreya, P. Ney, Branching Processes, Springer, New York, 1972. | MR | Zbl

[4] T.E. Harris, The Theory of Branching Processes, Springer, Heidelberg, 1963. | MR | Zbl

[5] P. Jagers, Branching Processes with Biological Applications, Wiley, London, 1975. | MR | Zbl

[6] S. Karlin, J. Mcgregor, Uniqueness of stationary measures for branching processes and applications, in: Proc. of the Fifth Berkeley Symposium, vol. II, Univ. of California Press, Berkeley, 1967, pp. 243-254. | MR | Zbl

[7] J.G. Kemeny, J.L. Snell, A.W. Knapp, Denumerable Markov Chains, Springer, New York, 1976. | MR | Zbl

[8] H. Kesten, P. Ney, F. Spitzer, The Galton-Watson process with mean one and finite variance, Theory Probab. Appl. 11 (1966) 513-540. | MR | Zbl

[9] J.F.C. Kingman, Stationary for branching processes, Proc. Amer. Math. Soc. 16 (1965) 245-247. | MR | Zbl

[10] F. Papangelou, A lemma on the Galton-Watson process and some of its consequences, Proc. Amer. Math. Soc. 19 (1968) 1469-1479. | MR | Zbl

[11] E. Seneta, The Galton-Watson process with mean one, J. Appl. Probab. 4 (1967) 489-495. | MR | Zbl

[12] F. Spitzer, Two explicit Martin boundary constructions, in: Symposium on Probab. Methods in Analysis, Lecture Notes in Math., vol. 31, Springer, Berlin, 1967, pp. 296-298. | MR | Zbl

Cité par Sources :