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

Hesong Wang, Zhiqiang Gao and Quansheng Liu

Statistics & Probability Letters, 2011, vol. 81, issue 5, 539-547

Abstract: For a supercritical branching process (Zn) in a stationary and ergodic environment [xi], we study the rate of convergence of the normalized population Wn=Zn/E[Zn[xi]] to its limit W[infinity]: we show a central limit theorem for W[infinity]-Wn 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 Wn+k-Wn for each fixed .

Keywords: Branching; processes; Random; environment; Central; limit; theorem; Martingale; Rate; of; convergence (search for similar items in EconPapers)
Date: 2011
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Citations: View citations in EconPapers (3)

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