Athreya, K.B.(1999): Growth rates of lines of descent in branching process may differ, preprint M99-12, Department of Mathematics, Iowa State University.  Home/Search   Document Not in Database   Summary   Related Articles

....n c n 1 m and c Gamma1 n Z n converges with probability 1 (w.p.1) to a finite random variable W that is nontrivial, is, P (W = 0jZ 0 = 1) q 1. The constants c n are called Senata Heyde constants and the result was first established by Senata [55] and strengthened by Heyde [39] Athreya [15] showed that if fZ n : n 1g and fZ 0 n : n 1gare two independent copies of branching processes, then Z Gamma1 n Z 0 n converges to a random variable W and if m 1 then P (0 W 1) 1;however if m = 1 then P (W = 0) and P (W = 1) are both positive. This says that in the infinite mean ....

Athreya, K.B.(1999): Growth rates of lines of descent in branching process may differ, preprint M99-12, Department of Mathematics, Iowa State University.

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