Abstract
We consider the regularity and ergodic properties of the Branching Collision Process with Immigration (BCIP) in this paper. We establish an easy checking sufficient condition under which the Feller minimal BCIP is honest. We provide some good conditions under which the Feller minimal BCIP is positive recurrent and then establish an analytic form of the generating function of the stationary distribution. The closely associated expected hitting times are also considered. Examples and numerical calculations are provided to illustrate our results.
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Acknowledgments
The work described in this paper by Anyue Chen was substantially supported by a local grant from the Southern University of Science and Technology and the work described in this paper by Junping Li was substantially supported by grants from the National Natural Sciences Foundation of China (No.11771452).
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Chen, A., Li, J. & Zhang, J. Branching Collision Processes with Immigration. Methodol Comput Appl Probab 22, 1063–1088 (2020). https://doi.org/10.1007/s11009-019-09745-1
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DOI: https://doi.org/10.1007/s11009-019-09745-1
Keywords
- Markov branching processes
- Collision branching processes
- Immigration
- Regularity
- Recurrence
- Positive recurrence
- Stationary distributions