On age-dependent branching processes with immigration

✍ Scribed by Ron Shonkwiler

• Publisher: Elsevier Science
• Year: 1980
• Tongue: English
• Weight: 485 KB
• Volume: 6
• Category: Article
• ISSN: 0898-1221
• DOI: 10.1016/0898-1221(80)90036-x

✦ Synopsis

We derive the probability generating function for the general Bellman-Harris age dependent branching process with immigration emphasizing the role of immigration parameters. The solution requires solving a single scalar-valued integral equation namely the usual Bellman-Harris equation. Our results are applied to three particular examples. We derive the equations for the immigration of particles governed by a Bellman-Harris process into a second Bellman-Harris process, In the second example we study Poisson immigration of particles into a time continuous Markov branching process. In the third, we derive the equations for a one-time immigration into a Bellman-Harris process.