Athreya,K.B.(1971): On the absolute continuity of the limit random variable in the supercritical Galton-Watson branching processes, Proceedings of the American Mathematical Society, 30, 563-565.  Home/Search   Document Not in Database   Summary   Related Articles

....will become clear later(see for instance Theorem 5 and Theorem 7) We now describe the fundamental limit theorems associated with supercritical branching processes. The first limit theorem describes the behavior of the branching process in the supercritical case. Kesten and Stigum [47] and Athreya [11]) Theorem 2. The sequence W n j Z n =m n (2.7) is a nonnegative martingale and hence converges with probability 1 (w.p.1) to a limit W . Further, i) P (W = 0jZ 0 = 1) is one or q according as 1 X 0 j(log j)p j = 1 or 1: 2.8) ii) If P 1 0 j(log j)p j 1 then E(W jZ 0 = 1) 1 and ....

Athreya,K.B.(1971): On the absolute continuity of the limit random variable in the supercritical Galton-Watson branching processes, Proceedings of the American Mathematical Society, 30, 563-565.

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