Asymptotic properties of supercritical branching processes in random environments |
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Authors: | Yingqiu Li Quansheng Liu Zhiqiang Gao Hesong Wang |
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Affiliation: | 1. College of Mathematics and Computing Sciences, Changsha University of Science and Technology, Changsha 410004, China2. Université de Bretagne-Sud, UMR 6205, LMBA, F-56000 Vannes, France3. School of Mathematical Sciences, Beijing Normal University, Beijing 100875, China |
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Abstract: | We consider a supercritical branching process (Zn) in an independent and identically distributed random environment ξ, and present some recent results on the asymptotic properties of the limit variable W of the natural martingale Wn=Zn/E[Zn|ξ], the convergence rates of W-Wn(by considering the convergence in law with a suitable norming, the almost sure convergence, the convergence in LP, and the convergence in probability), and limit theorems (such as central limit theorems, moderate and large deviations principles) on (log Zn). |
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Keywords: | Branching process random environment large deviation moderate deviation central limit theorem moment weighted moment convergence rate |
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