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Article Dans Une Revue Statistics and Probability Letters Année : 2011

Central limit theorems for a supercritical branching process in a random environment

Résumé

For a supercritical branching process $(Z_n)$ in a stationary and ergodic environment $\xi$, we study the rate of convergence of the normalized population $W_n= Z_n/E[Z_n|\xi]$ to its limit $W_\infty$: we show a central limit theorem for $W_{\infty}-W_n$ with suitable normalization and derive a Berry-Esseen bound for the rate of convergence in the central limit theorem when the environment is independent and identically distributed. Similar results are also shown for $W_{n+k}-W_n$ for each fixed $k \in \mathbb{N}^*$.
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Dates et versions

hal-00907157 , version 1 (21-11-2013)

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Hesong Wang, Zhiqiang Gao, Quansheng Liu. Central limit theorems for a supercritical branching process in a random environment. Statistics and Probability Letters, 2011, 81 (5), pp.539-547. ⟨10.1016/j.spl.2011.01.003⟩. ⟨hal-00907157⟩
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