Central limit theorems for a supercritical branching process in a random environment
نویسندگان
چکیده
For a supercritical branching process (Zn) in a stationary and ergodic environment ξ, we study the rate of convergence of the normalized population Wn = Zn/E[Zn|ξ] to its limitW∞: we show a central limit theorem forW∞−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 k ∈ N.
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