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Asymptotic properties of supercritical branching processes in random environments
Yingqiu LI,Quansheng LIU,Zhiqiang GAO,Hesong WANG
Front. Math. China. 2014, 9 (4): 737-751.
https://doi.org/10.1007/s11464-014-0397-z
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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