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. 
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     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://www.numdam.org/articles/10.1016/j.anihpb.2006.03.001/}
}
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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://www.numdam.org/articles/10.1016/j.anihpb.2006.03.001/

[1] A. Asmussen, H. Hering, Branching Processes, Progress in Probab. and Statistics, vol. 3, Birkhäuser Boston Inc., Boston, MA, 1983. | MR | Zbl

[2] K.B. Athreya, P.E. Ney, The local limit theorem and some related aspects of supercritical branching processes, Trans. Amer. Math. Soc. 152 (2) (1970) 233-251. | MR | Zbl

[3] J.D. Biggins, N.H. Bingham, Near-constancy phenomena in branching processes, Math. Proc. Cambridge Philos. Soc. 110 (3) (1991) 545-558. | MR | Zbl

[4] J.D. Biggins, N.H. Bingham, Large deviations in the supercritical branching process, Adv. Appl. Probab. 25 (4) (1993) 757-772. | MR | Zbl

[5] N.H. Bingham, On the limit of a supercritical branching process, J. Appl. Probab. 25A (1988) 215-228. | MR | Zbl

[6] S. Dubuc, La densite de la loi-limite d'un processus en cascade expansif, Z. Wahrsch. Verw. Gebiete 19 (1971) 281-290. | MR | Zbl

[7] S. Dubuc, Etude theorique et numerique de la fonction de Karlin-McGregor, J. Analyse Math. 42 (1982) 15-37. | Zbl

[8] S. Dubuc, E. Seneta, The local limit theorem for the Galton-Watson process, Ann. Probab. 4 (1976) 490-496. | Zbl

[9] W. Feller, An Introduction to Probability Theory and its Applications, vol. II, second ed., John Wiley and Sons, New York, 1971. | MR | Zbl

[10] K. Fleischmann, V. Wachtel, 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] R. Höpfner, Local limit theorems for non-critical Galton-Watson processes with or without immigration, J. Appl. Probab. 19 (1982) 262-271. | Zbl

[13] M. Kuczma, Functional Equations in a Single Variable, PWN, Warszaw, 1968. | MR | Zbl

[14] P.E. Ney, A.N. Vidyashankar, Local limit theory and large deviations for supercritical branching processes, Ann. Appl. Probab. 14 (2004) 1135-1166. | MR | Zbl

[15] V.V. Petrov, Sums of Independent Random Variables, Springer-Verlag, Berlin, 1975. | MR | Zbl

[16] E. Seneta, Regularly Varying Functions, Lecture Notes in Math., vol. 508, Springer-Verlag, Berlin, 1976. | MR | Zbl

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