On calculating extinction probabilities for branching processes in random environments
- 1 April 1969
- journal article
- research article
- Published by Cambridge University Press (CUP) in Journal of Applied Probability
- Vol. 6 (03) , 478-492
- https://doi.org/10.1017/s0021900200026553
Abstract
Consider a discrete time Markov chain {Zn } whose state space is the non-negative integers and whose transition probability matrix ║Pij ║ possesses the representation where {Pr }, r = 1,2,…, is a finite or denumerably infinite sequence of non-negative real numbers satisfying , and , is a corresponding sequence of probability generating functions. It is assumed that Z 0 = k, a finite positive integer.Keywords
This publication has 2 references indexed in Scilit:
- On Branching Processes in Random EnvironmentsThe Annals of Mathematical Statistics, 1969
- Necessary Conditions for Almost Sure Extinction of a Branching Process with Random EnvironmentThe Annals of Mathematical Statistics, 1968