Recurrence and transience of critical branching processes in random environment with immigration and an application to excited random walks. (English) Zbl 1303.60075
Summary: We establish recurrence and transience criteria for critical branching processes in random environments with immigration. These results are then applied to the recurrence and transience of a recurrent random walk in a random environment on Z disturbed by cookies inducing a drift to the right of strength 1.
This paper complements [E. Bauernschubert, Ann. Inst. Henri Poincaré, Probab. Stat. 49, No. 3, 638–653 (2013; Zbl 1274.60254)].
This paper complements [E. Bauernschubert, Ann. Inst. Henri Poincaré, Probab. Stat. 49, No. 3, 638–653 (2013; Zbl 1274.60254)].
MSC:
| 60J80 | Branching processes (Galton-Watson, birth-and-death, etc.) |
| 60J85 | Applications of branching processes |
| 60K37 | Processes in random environments |
Keywords:
critical branching process in a random environment with immigration; excited random walk in a random environment; cookies of strength 1; recurrence; transienceCitations:
Zbl 1274.60254References:
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