ON THE SURVIVAL PROBABILITY OF A BRANCHING-PROCESS IN A RANDOM ENVIRONMENT

Authors
DSOUZA JC HAMBLY BM
Citation
Jc. Dsouza et Bm. Hambly, ON THE SURVIVAL PROBABILITY OF A BRANCHING-PROCESS IN A RANDOM ENVIRONMENT, Advances in Applied Probability, 29(1), 1997, pp. 38-55
Citations number
16
Categorie Soggetti
Statistic & Probability","Statistic & Probability
Journal title
Advances in Applied Probability → ACNP
ISSN journal
00018678
Volume
29
Issue
1
Year of publication
1997
Pages
38 - 55
Database
ISI
SICI code
0001-8678(1997)29:1<38:OTSPOA>2.0.ZU;2-C
Abstract
We derive a variety of estimates for the survival probability of a bra nching process in a random environment. There are three cases of inter est, the critical, weakly and strongly subcritical. The large deviatio n result, first obtained by Dekking for the class of finite state spac e i.i.d. environments, is shown to hold in more general environments. We also obtain some finer convergence results.