On the extinction times of varying and random environment branching processes
- 1 March 1975
- journal article
- research article
- Published by Cambridge University Press (CUP) in Journal of Applied Probability
- Vol. 12 (01) , 39-46
- https://doi.org/10.1017/s0021900200033076
Abstract
Bounds are derived for the probability of extinction by the nth generation for a branching process in a varying environment. From these bounds, necessary and sufficient conditions are established for such a process to become extinct with probability one. The extinction time of a random environment branching process in which the environmental random variables are independent but not necessarily identically distributed is stochastically bounded by the extinction times of two varying environment processes.Keywords
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