@article{AIHPB_2007__43_2_233_0, author = {Fleischmann, Klaus and Wachtel, Vitali}, title = {Lower deviation probabilities for supercritical {Galton-Watson} processes}, journal = {Annales de l'I.H.P. Probabilit\'es et statistiques}, pages = {233--255}, publisher = {Elsevier}, volume = {43}, number = {2}, year = {2007}, doi = {10.1016/j.anihpb.2006.03.001}, zbl = {1112.60066}, language = {en}, url = {http://archive.numdam.org/articles/10.1016/j.anihpb.2006.03.001/} }
TY - JOUR AU - Fleischmann, Klaus AU - Wachtel, Vitali TI - Lower deviation probabilities for supercritical Galton-Watson processes JO - Annales de l'I.H.P. Probabilités et statistiques PY - 2007 SP - 233 EP - 255 VL - 43 IS - 2 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/j.anihpb.2006.03.001/ DO - 10.1016/j.anihpb.2006.03.001 LA - en ID - AIHPB_2007__43_2_233_0 ER -
%0 Journal Article %A Fleischmann, Klaus %A Wachtel, Vitali %T Lower deviation probabilities for supercritical Galton-Watson processes %J Annales de l'I.H.P. Probabilités et statistiques %D 2007 %P 233-255 %V 43 %N 2 %I Elsevier %U http://archive.numdam.org/articles/10.1016/j.anihpb.2006.03.001/ %R 10.1016/j.anihpb.2006.03.001 %G en %F AIHPB_2007__43_2_233_0
Fleischmann, Klaus; Wachtel, Vitali. Lower deviation probabilities for supercritical Galton-Watson processes. Annales de l'I.H.P. Probabilités et statistiques, Tome 43 (2007) no. 2, pp. 233-255. doi : 10.1016/j.anihpb.2006.03.001. http://archive.numdam.org/articles/10.1016/j.anihpb.2006.03.001/
[1] Branching Processes, Progress in Probab. and Statistics, vol. 3, Birkhäuser Boston Inc., Boston, MA, 1983. | MR | Zbl
, ,[2] The local limit theorem and some related aspects of supercritical branching processes, Trans. Amer. Math. Soc. 152 (2) (1970) 233-251. | MR | Zbl
, ,[3] Near-constancy phenomena in branching processes, Math. Proc. Cambridge Philos. Soc. 110 (3) (1991) 545-558. | MR | Zbl
, ,[4] Large deviations in the supercritical branching process, Adv. Appl. Probab. 25 (4) (1993) 757-772. | MR | Zbl
, ,[5] On the limit of a supercritical branching process, J. Appl. Probab. 25A (1988) 215-228. | MR | Zbl
,[6] La densite de la loi-limite d'un processus en cascade expansif, Z. Wahrsch. Verw. Gebiete 19 (1971) 281-290. | MR | Zbl
,[7] Etude theorique et numerique de la fonction de Karlin-McGregor, J. Analyse Math. 42 (1982) 15-37. | Zbl
,[8] The local limit theorem for the Galton-Watson process, Ann. Probab. 4 (1976) 490-496. | Zbl
, ,[9] vol. II, second ed., John Wiley and Sons, New York, 1971. | MR | Zbl
, An Introduction to Probability Theory and its Applications,[10] Lower deviation probabilities for supercritical Galton-Watson processes, WIAS Berlin, Preprint No. 1025 of April 28, 2005, http://www.wias-berlin.de/publications/preprints/1025/.
, ,[11] K. Fleischmann, V. Wachtel, Large deviations for sums defined on a Galton-Watson process, WIAS Berlin, Preprint No. 1135 of May 29, 2006.
[12] Local limit theorems for non-critical Galton-Watson processes with or without immigration, J. Appl. Probab. 19 (1982) 262-271. | Zbl
,[13] Functional Equations in a Single Variable, PWN, Warszaw, 1968. | MR | Zbl
,[14] Local limit theory and large deviations for supercritical branching processes, Ann. Appl. Probab. 14 (2004) 1135-1166. | MR | Zbl
, ,[15] Sums of Independent Random Variables, Springer-Verlag, Berlin, 1975. | MR | Zbl
,[16] Regularly Varying Functions, Lecture Notes in Math., vol. 508, Springer-Verlag, Berlin, 1976. | MR | Zbl
,Cité par Sources :