A condition for the extinction of a branching process with an absorbing lower barrier

✍ Scribed by H. -J. Schuh

• Publisher: Springer
• Year: 1976
• Tongue: English
• Weight: 580 KB
• Volume: 3
• Category: Article
• ISSN: 0303-6812
• DOI: 10.1007/bf00275060

✦ Synopsis

A branching process with an absorbing lower barrier is considered. This is a Galton-Watson process with the condition that at any generation the number of individuals is greater than a lower barrier or it is equal to zero (i.e. all individuals in populations which are too small die and have no offspring). A necessary and sufficient condition is given for the process to become extinct with probability one. At the end of the paper there are three illustrating examples.