An asymptotic expansion for the expectation of an age-dependent branching process with a submultiplicative estimate of the remainder

Journal of Applied Probability

Volumn 38, Issue 3, 2001, Pages 807-814

  Sgibnev, M S ^a  

^a SOBOLEV INSTITUTE OF MATHEMATICS   (Russian Federation)

Author keywords

Absolutely continuous part; Age dependence; Asymptotic behaviour; Branching process; Characteristic equation; Expectation; Laplace transform; Malthusian parameter; Renewal theorem; Submultiplicative function

Indexed keywords

EID: 0035438336     PISSN: 00219002     EISSN: None     Source Type: Journal    
DOI: 10.1239/jap/1005091046     Document Type: Article

References (9)

1. ATHREYA, K. B. AND NEY, P. E. (1972). Branching Processes. Springer, Berlin.
2. CHOVER, J., NEY, P. AND WAINGER, S. (1973). Degeneracy properties of subcritical branching processes. Ann. Prob. 1, 663-673.
3. FELLER, W. (1966). An Introduction to Probability Theory and Its Applications II. John Wiley, New York.
4. HARRIS, T. E. (1963). The Theory of Branching Processes. Springer, Berlin.
5. HILLE, E. AND PHILLIPS, R. S. (1957). Functional Analysis and Semi-Groups (Amer. Math. Soc. Colloq. Publ. 31). American Mathematical Society, Providence, RI.
6. SGIBNEV, M. S. (1991). Exponential estimates of the rate of convergence for the higher renewal moments. Siberian Math. J. 32, 657-664.
7. SGIBNEV, M. S. (1997). Submultiplicative moments of the supremum of a random walk with negative drift. Statist. Prob. Lett. 32, 377-383.
8. SGIBNEV, M. S. (2000). An asymptotic expansion for the distribution of the supremum of a random walk. Studia Math. 140, 41-55.
9. VAN DER GENUGTEN, B. B. (1969). Asymptotic expansions in renewal theory. Compositio Math. 21, 331-342.