A Note on Multitype Branching Process with Bounded Immigration in Random Environment  

作　　者：Hua Ming WANG 

机构地区：[1]Department of Mathematics, Anhui Normal University

出　　处：《Acta Mathematica Sinica,English Series》2013年第6期1095-1110,共16页数学学报（英文版）

基　　金：Supported by National Nature Science Foundation of China(Grant No.11226199)

摘　　要：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）＂）.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）＂）.

关 键 词：Branching process random walk random environment 

分 类 号：O211.65[理学—概率论与数理统计]