Local limit theory and large deviations for supercritical Branching processes
Peter E. Ney, Anand N. Vidyashankar
Abstract
In this paper we study several aspects of the growth of a supercritical Galton-Watson process Zn:n1, and bring out some criticality phenomena determined by the Schroder 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:n1, where Yn satisfies an LDP, particularly of Zn-1Zn+1:n1 conditioned on Zn vn.
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