A note on multitype branching process with bounded immigration in random environment |
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Authors: | Hua Ming Wang |
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Institution: | 11350. Department of Mathematics, Anhui Normal University, Wuhu, 241000, P. R. China
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Abstract: | In this paper, we study the total number of progeny, W, before regenerating of multitype branching process with immigration in random environment. We show that the tail probability of |W| is of order t ?κ as t → ∞, with κ some constant. As an application, we prove a stable law for (L-1) random walk in random environment, generalizing the stable law for the nearest random walk in random environment (see “Kesten, Kozlov, Spitzer: A limit law for random walk in a random environment. Compositio Math., 30, 145–168 (1975)”). |
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Keywords: | Branching process random walk random environment |
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