Abstract
In this paper we study several aspects of the growth of a supercritical Galton–Watson process {Zn:n≥1}, and bring out some criticality phenomena determined by the Schröder constant. We develop the local limit theory of Zn, that is, the behavior of P(Zn=vn) as vn↗∞, and use this to study conditional large deviations of {YZn:n≥1}, where Yn satisfies an LDP, particularly of {Zn−1Zn+1:n≥1} conditioned on Zn≥vn.
Citation
Peter E. Ney. Anand N. Vidyashankar. "Local limit theory and large deviations for supercritical Branching processes." Ann. Appl. Probab. 14 (3) 1135 - 1166, August 2004. https://doi.org/10.1214/105051604000000242
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