Geodesic
Limit theorems for critical Markov branching processes with several types of particles and infinite second moments
Sbornik. Mathematics, Tome 32 (1977) no. 2, pp. 215-225 
V. A. Vatutin. Limit theorems for critical Markov branching processes with several types of particles and infinite second moments. Sbornik. Mathematics, Tome 32 (1977) no. 2, pp. 215-225. http://geodesic.mathdoc.fr/item/SM_1977_32_2_a2/
@article{SM_1977_32_2_a2,
     author = {V. A. Vatutin},
     title = {Limit theorems for critical {Markov} branching processes with several types of particles and infinite second moments},
     journal = {Sbornik. Mathematics},
     pages = {215--225},
     year = {1977},
     volume = {32},
     number = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1977_32_2_a2/}
}
TY  - JOUR
AU  - V. A. Vatutin
TI  - Limit theorems for critical Markov branching processes with several types of particles and infinite second moments
JO  - Sbornik. Mathematics
PY  - 1977
SP  - 215
EP  - 225
VL  - 32
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/SM_1977_32_2_a2/
LA  - en
ID  - SM_1977_32_2_a2
ER  - 
%0 Journal Article
%A V. A. Vatutin
%T Limit theorems for critical Markov branching processes with several types of particles and infinite second moments
%J Sbornik. Mathematics
%D 1977
%P 215-225
%V 32
%N 2
%U http://geodesic.mathdoc.fr/item/SM_1977_32_2_a2/
%G en
%F SM_1977_32_2_a2

Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper a necessary and sufficient condition is obtained for the existence of a proper limit distribution, not concentrated at one point, of the number of particles in a critical Markov branching process with several types of particles on the set of nondegenerate trajectories under the classical normalization. In the case where the limit distribution in question exists, limit distributions for the distance to the nearest common ancestor are obtained. Bibliography: 10 titles.

[1] B. A. Sevastyanov, Vetvyaschiesya protsessy, izd-vo «Nauka», Moskva, 1971 | MR

[2] V. M. Zolotarev, “Utochnenie ryada teorem teorii vetvyaschikhsya sluchainykh protsessov”, Teoriya veroyatn., II:2 (1957), 256–266 | MR

[3] E. Seneta, Slowly varying functions, Lecture Notes in Math., 508, Springer-Verlag, Heidelberg, 1976 | MR | Zbl

[4] V. Feller, Vvedenie v teoriyu veroyatnostei i ee prilozheniya, t. II, izd-vo «Mir», Moskva, 1967

[5] R. S. Slack, “A branching process with mean one and possibly infinite variance”, Z. Wahrscheinlichkeitstheorie verw. Geb., 9:2 (1968), 139–145 | DOI | MR | Zbl

[6] R. S. Slack, “Futher notes on branching process with mean one”, Z. Wahrscheinlichkeitstheorie verw. Geb., 25:1 (1972), 31–38 | DOI | MR | Zbl

[7] A. M. Zubkov, “Predelnye raspredeleniya rasstoyaniya do blizhaishego obschego predka”, Teoriya veroyatn., XX:3 (1975), 614–623 | MR

[8] K. B. Athreya, P. E. Ney, Branching processes, Springer-Verlag, Heidelberg, 1972 | MR | Zbl

[9] T. Kharris, Teoriya vetvyaschikhsya sluchainykh protsessov, izd-vo «Mir», Moskva, 1966

[10] R. Ganing, Kh. Rossi, Analiticheskie funktsii mnogikh kompleksnykh peremennykh, izd-vo «Mir», Moskva, 1969 | MR