The survival probability of a critical branching process in a random environment

Theory of Probability and its Applications

Volumn 45, Issue 3, 2000, Pages 517-525

  Geiger, J ^a   Kersting, G ^a  

^a GOETHE UNIVERSITY   (Germany)

Author keywords

Branching processes; Conditioned random walks; Random environments

Indexed keywords

EID: 0034563393     PISSN: 0040585X     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0040585X97978440     Document Type: Article

References (13)

1. V. I. AFANASYEV, Limit theorems for a moderately subcritical branching process in a random environment, Discrete Math. Appl., 8 (1998), pp. 35-52.
2. A. AGRESTI, On the extinction times of varying and random environment branching processes, J. Appl. Probab., 12 (1975), pp. 39-46.
3. K. B. ATHREYA AND S. KARLIN, On branching processes with random environments: I, II, Ann. Math. Statist., 42 (1971), pp. 1499-1520; pp. 1843-1858.
4. J. BERTOIN AND R. A. DONEY, On conditioning a random walk to stay positive, Ann. Probab., 22 (1994), pp. 2152-2167.
5. J. S. D'SOUZA AND B. M. HAMBLY, On the survival probability of a branching process in a random environment, Adv. Appl. Probab., 29 (1997), pp. 38-55.
6. W. FELLER, An Introduction to Probability Theory and Its Applications, Vol. II, Wiley, New York, 1971.
7. J. GEIGER, Elementary new proofs of classical limit theorems for Gallon-Watson processes, J. Appl. Probab., 36 (1999), pp. 301-309.
8. K. HIRANO, Determination of the limiting coefficient for exponential functionals of random walks with positive drift, J. Math. Sci. Univ. Tokyo. 5 (1998), pp. 299-332.
9. H. KESTEN, P. NEY, AND F. SPITZER, The Galton-Watson process with mean one and finite variance, Theory Probab. Appl., 11 (1966), pp. 513-540.
10. 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), pp. 791-804.
11. W. L. SMITH AND W. E. WILKINSON, On branching processes in random environments, Ann. Math. Statist., 40 (1969), pp. 814-827.
12. V. A. VATUTIN AND E. E. DYAKONOVA, Critical branching processes in random environment: The probability of extinction at a given moment, Discrete Math. Appl., 7 (1997), pp. 469-496.
13. V. A. VATUTIN AND A. M. ZUBKOV, Branching Processes II, J. Sov. Math., 67 (1993), pp. 3407-3485.