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Article Dans Une Revue Frontiers of Mathematics in China Année : 2014

Supercritical branching processes in random environments

Résumé

We consider a supercritical branching process $(Z_n)$ in an independent and identically distributed random environment $\xi$, and present some recent results on the asymptotic properties of the limit variable $W$ of the natural martingale $W_n= Z_n/\mathbb{E}[Z_n|\xi]$, the convergence rates of $W - W_n $ (by considering the convergence in law with a suitable norming, the almost sure convergence, the convergence in $L^p$ and the convergence in probability), and limit theorems (such as central limit theorems, moderate and large deviations principles) on ($\log Z_n$).
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Dates et versions

hal-01095070 , version 1 (15-12-2014)

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Yingqiu Li, Zhiqiang Cao, Quansheng Liu, Hesong Wang. Supercritical branching processes in random environments. Frontiers of Mathematics in China, 2014, 9 (4), pp.835-842. ⟨10.1007/s11464-014-0397-z⟩. ⟨hal-01095070⟩
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