@MISC{Piau_onthe, author = {Didier Piau}, title = {On the Harmonic Means of Branching Processes}, year = {} }

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Abstract

The random variable X plays the role of 1 + Z in the eBMP context. Thus, m corresponds to 1 + = (1 p) 1 , and p 1 in this note is p 0 in Piau (2001b), and so on. 0.2 Results Joe (1993) mentions, as an unpublished result, the fact that, for any a > 0, E (S a n ) 6 c q n for any q > maxfp 1 ; m a g; where c is independent of n. In the same vein, Athreya (1994) shows that, if p 1 m a > 1, then p n 1 E(S a n j S 0 = 1) is a nondecreasing sequence, t