Abstract
Let Z n (n=0, l, ...) be an aperiodic critical Galton-Watson process and let σ 2 be the (possibly infinite) variance of Z 1. Let η k (k=1, 2, ...) denote the stationary measure of the process. Kesten, Ney and Spritzer proved in 1966 that η k →2/σ 2 as k→∞ (*) under the additional assumption that EZ 21 log Z 1<∞ (**) In the present paper, (*) is proved without the assumption (**). The proof uses complex function theory.
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Pommerenke, C. On the stationary measures of critical branching processes. Z. Wahrscheinlichkeitstheorie verw Gebiete 55, 305–312 (1981). https://doi.org/10.1007/BF00532122
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DOI: https://doi.org/10.1007/BF00532122