Nonlinear Markov branching processes with immigration and resurrection

Abstract

Abstract The nonlinear Markov branching process with immigration and resurrection (NMBPIR) is considered in this paper. We give the criteria for regularity and uniqueness of NMBPIR, and then investigate the extinction probability and the mean extinction time. Furthermore, we give a condition for the Feller minimal NMBPIR to be recurrence, and provide an example to illustrate our results.

Keywords

• Nonlinear Markov branching process
• Regularity
• Resurrection
• Immigration
• Extinction probability