Moments, moderate and large deviations for a branching process in a random environment
Let (Zn) be a supercritical branching process in a random environment ξ, and W be the limit of the normalized population size Zn/E[Zn|ξ]. We show large and moderate deviation principles for the sequence logZn (with appropriate normalization). For the proof, we calculate the critical value for the existence of harmonic moments of W, and show an equivalence for all the moments of Zn. Central limit theorems on W−Wn and logZn are also established.
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Volume (Year): 122 (2012)
Issue (Month): 2 ()
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- Wang, Hesong & Gao, Zhiqiang & Liu, Quansheng, 2011. "Central limit theorems for a supercritical branching process in a random environment," Statistics & Probability Letters, Elsevier, vol. 81(5), pages 539-547, May.
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- Afanasyev, V.I. & Geiger, J. & Kersting, G. & Vatutin, V.A., 2005. "Functional limit theorems for strongly subcritical branching processes in random environment," Stochastic Processes and their Applications, Elsevier, vol. 115(10), pages 1658-1676, October.
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