Moments, moderate and large deviations for a branching process in a random environment |
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Authors: | Chunmao Huang Quansheng Liu |
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Institution: | LMAM, Université de Bretagne-Sud, Campus de Tohannic, BP 573, 56017 Vannes, France Université Européenne de Bretagne, France |
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Abstract: | Let (Zn) be a supercritical branching process in a random environment ξ, and W be the limit of the normalized population size Zn/EZn|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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Keywords: | 60J80 60K37 60F10 |
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