Moments, moderate and large deviations for a branching process in a random environment

By Chunmao Huang, Quansheng Liu. 2010

78 citations recorded by the source corpus.

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.

Subfields: Artificial Intelligence, Mathematical Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/1fc30a36d1e54a95cd6b91d22dc5781403aec3e1