Branching Collision Processes with Immigration

Anyue Chen (), Junping Li () and Jing Zhang ()
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Anyue Chen: The Southern University of Science and Technology
Junping Li: Central South University
Jing Zhang: The Southern University of Science and Technology

Methodology and Computing in Applied Probability, 2020, vol. 22, issue 3, 1063-1088

Abstract: 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.

Keywords: Markov branching processes; Collision branching processes; Immigration; Regularity; Recurrence; Positive recurrence; Stationary distributions; Primary 60J27; Secondary 60J35 (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s11009-019-09745-1

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