La σ-algèbre asymptotique d’une chaîne de Galton-Watson
Lootgieter, J. C.
Annales de l'I.H.P. Probabilités et statistiques, Tome 13 (1977), p. 193-230 / Harvested from Numdam
Access to full text
Full (PDF)
Full (DJVU)
Publié le : 1977-01-01
@article{AIHPB_1977__13_3_193_0,
     author = {Lootgieter, Jean-Claude},
     title = {La $\sigma $-alg\`ebre asymptotique d'une cha\^\i ne de Galton-Watson},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     volume = {13},
     year = {1977},
     pages = {193-230},
     zbl = {0382.60091},
     language = {fr},
     url = {http://dml.mathdoc.fr/item/AIHPB_1977__13_3_193_0}
}

Lootgieter, J. C. La $\sigma $-algèbre asymptotique d’une chaîne de Galton-Watson. Annales de l'I.H.P. Probabilités et statistiques, Tome 13 (1977) pp. 193-230. http://gdmltest.u-ga.fr/item/AIHPB_1977__13_3_193_0/

[1] A. Abrahamse, The tail field of a Markov Chain. Ann. Statistic, t. 40, 1969, p. 127-136. | MR 248913 | Zbl 0181.44805

[2] K.B. Athreya, A note on a functional equation arising in Galton-Watson branching processes. Journal Applied Probability, t. 8, 1971, p. 589-598. | MR 292184 | Zbl 0254.60058

[3] K.B. Athreya, On the absoluty continuity of the limit random variable in the supercritical Galton-Watson process. Proceedings of American Math. Society, t. 30, 1971, p. 563-565. | MR 282421 | Zbl 0234.60097

[4] K.B. Athreya, P. Ney, Branching processes. Berlin, Springer, 1972. | MR 373040 | Zbl 0259.60002

[5] H. Cohn, On the tail events of a Markov Chain. Z. Wahrscheinlichkeitstheorie verw. gebiete, t. 29, 1974, p. 65-72. | MR 362495 | Zbl 0279.60051

[6] S. Dubuc, Positive harmonic functions of branching processes. Proceedings of the American Math. Society, t. 21, 1969, p. 324-326. | MR 251800 | Zbl 0176.47601

[7] S. Dubuc, La fonction de Green d'un processus de Galton-Watson. Studia Math., t. 34, 1970, p. 69-87. | MR 260042 | Zbl 0196.18802

[8]. S. Dubuc, Problèmes relatifs à l'itération des fonctions suggérés par les processus en cascade. Ann. Inst. Fourier, Grenoble, t. 21, 1971, p. 171-251. | Numdam | MR 297025 | Zbl 0196.12801

[9] I. Guelfand, D. Raikov, Q. Shilov, Commutative normed rings, Chelsea, 1964.

[10] T.E. Harris, The theory of branching processes. Berlin, Springer. | MR 163361 | Zbl 0117.13002

[11] C.C. Heyde, Extension of a result of Seneta for the supercritical Galton-Watson process. Ann. Math. Statistics, t. 41, 1970, p. 739-742. | MR 254929 | Zbl 0195.19201

[12] J.C. Lootgieter, Processus de Galton-Watson de moyenne 1. C. R. Acad. Sci., Paris, avril 1969, t. 268, Série A, p. 817-818. | MR 242278 | Zbl 0269.60065

[13] J. Neveu, Chaînes de Markov et théorie du potentiel. Annales Fac. Sci., Clermont-Ferrand, t. 24, 1964, p. 37-89. | Numdam | MR 386031

[14] D.J. Newmann, J.T. Schwartz, H.S. Shapiro, On generators of the Banach algebras l1 et L1(0, + ∞). Trans. Amer. Math. Soc., t. 107, 1963, p. 466-484. | MR 150579 | Zbl 0117.09301

[15] W. Rudin, Real and complex analysis. McGraw-Hill, 1966. | MR 210528 | Zbl 0142.01701

[16] W. Rudin, Fourier analysis on groups. Interscience publishers, 1967.

[17] E. Seneta, On recents theorems concerning the supercritical Galton-Watson process. Ann. Math. Statistics, t. 39, 1968, p. 2098-2102. | MR 234530 | Zbl 0176.47603

[18] E. Seneta, Functionals equations and the Galton-Watson process. Adv. Appl. Prob., t. 1, 1969, p. 1-42. | MR 248917 | Zbl 0183.46105

[19] E. Seneta, Regularly varying functions in the theory of simple branching processes. Vol. 6, n° 3, septembre 1974. | MR 420894 | Zbl 0291.60043