Limit theorems for subcritical branching processes in random environment
Annales de l'I.H.P. Probabilités et statistiques, Tome 39 (2003) no. 4, pp. 593-620. 
@article{AIHPB_2003__39_4_593_0,
     author = {Geiger, Jochen and Kersting, G\"otz and Vatutin, Vladimir A.},
     title = {Limit theorems for subcritical branching processes in random environment},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     pages = {593--620},
     publisher = {Elsevier},
     volume = {39},
     number = {4},
     year = {2003},
     doi = {10.1016/S0246-0203(02)00020-1},
     zbl = {1038.60083},
     language = {en},
     url = {http://archive.numdam.org/articles/10.1016/S0246-0203(02)00020-1/}
}
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Geiger, Jochen; Kersting, Götz; Vatutin, Vladimir A. Limit theorems for subcritical branching processes in random environment. Annales de l'I.H.P. Probabilités et statistiques, Tome 39 (2003) no. 4, pp. 593-620. doi : 10.1016/S0246-0203(02)00020-1. http://archive.numdam.org/articles/10.1016/S0246-0203(02)00020-1/

[1] V.I. Afanasyev, Limit theorems for a conditional random walk and some applications. Diss. Cand. Sci., Moscow, MSU, 1980.

[2] V.I. Afanasyev, Limit theorems for a moderately subcritical branching process in a random environment, Discrete Math. Appl. 8 (1998) 35-52. | MR | Zbl

[3] A. Agresti, Bounds on the extinction time distribution of a branching process, Adv. Appl. Probab. 6 (1974) 322-335. | MR | Zbl

[4] K.B. Athreya, S. Karlin, On branching processes with random environments: I, II, Ann. Math. Stat. 42 (1971) 1499-1520, 1843-1858. | Zbl

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

[6] J. Bertoin, R.A. Doney, On conditioning a random walk to stay positive, Ann. Probab. 22 (1994) 2152-2167. | MR | Zbl

[7] F.M. Dekking, On the survival probability of a branching process in a finite state i.i.d. environment, Stochastic Processes Appl. 27 (1988) 151-157. | MR | Zbl

[8] R.A. Doney, On the asymptotic behaviour of first passage times for transient random walk, Probab. Theory Related Fields 81 (1989) 239-246. | MR | Zbl

[9] J.S. D'Souza, B.M. Hambly, On the survival probability of a branching process in a random environment, Adv. Appl. Probab. 29 (1997) 38-55. | MR | Zbl

[10] W. Feller, An Introduction to Probability Theory and Its Applications, Vol. II, Wiley, New York, 1971. | MR | Zbl

[11] K. Fleischmann, V.A. Vatutin, Reduced subcritical Galton-Watson processes in a random environment, Adv. Appl. Probab. 31 (1999) 88-111. | Zbl

[12] J. Geiger, Elementary new proofs of classical limit theorems for Galton-Watson processes, J. Appl. Probab. 36 (1999) 301-309. | Zbl

[13] J. Geiger, G. Kersting, The survival probability of a critical branching process in random environment, Teor. Verojatnost. i Primenen. 45 (2000) 607-615. | MR | Zbl

[14] Y. Guivarc'H, Q. Liu, Propriétés asymptotiques des processus de branchement en environnement aléatoire, C. R. Acad. Sci. Paris Sér. I Math. 332 (4) (2001) 339-344. | MR | Zbl

[15] K. Hirano, Determination of the limiting coefficient for exponential functionals of random walks with positive drift, J. Math. Sci. Univ. Tokyo 5 (1998) 299-332. | MR | Zbl

[16] O. Kallenberg, Foundations of Modern Probability, Springer, New York, 1997. | MR | Zbl

[17] M.V. Kozlov, On the asymptotic behavior of the probability of non-extinction for critical branching processes in a random environment, Theory Probab. Appl. 21 (1976) 791-804. | MR | Zbl

[18] Q. Liu, On the survival probability of a branching process in a random environment, Ann. Inst. H. Poincaré Probab. Statist. 32 (1996) 1-10. | Numdam | MR | Zbl

[19] W.L. Smith, W.E. Wilkinson, On branching processes in random environments, Ann. Math. Stat. 40 (1969) 814-827. | MR | Zbl

[20] N. Veraverbeke, J.L. Teugels, The exponential rate of convergence of the distribution of the maximum of a random walk. Part II, J. Appl. Probab. 13 (1976) 733-740. | MR | Zbl

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