Local Limit Theory and Large Deviations for Supercritical Branching Processes


Let {Zn, n > 1} be a single type Galton-Watson process initiated by a single ancestor with mean EZ1 º m. This paper develops the local limit theory of Zn, viz., the behavior of P(Zn = vn) for 0 < vn ­ ¥ as n ® ¥. These results are used to study the large deviations of {Zn+1/Zn: n > 1} conditioned on Zn > vn. Some general questions on averages indexed by random sequences are discussed.

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