Local Limit Theory and Large Deviations for Supercritical Branching Processes
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چکیده
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 ր ∞, and use this to study conditional large deviations of {YZn :n ≥ 1}, where Yn satisfies an LDP, particularly of {Z −1 n Zn+1 :n ≥ 1} conditioned on Zn ≥ vn.
منابع مشابه
Corrections and Acknowledgment for “ Local Limit Theory and Large Deviations for Supercritical Branching Processes
Theorem 1 in [2] is incorrect in the case α ≥ 1. Our error stems from the fact that the lower bound C 1 was determined by an integral expression which we treated as positive, whereas in fact it was zero. This led to an incorrect normalization A n when α ≥ 1. This error was communicated to us by K. Fleischmann and V. Wachtel, and the correction, that A n = p n 1 v (α−1) n for all 0 < α < ∞, appe...
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تاریخ انتشار 2008