Athreya,K.B. and Kaplan,N.(1976): Convergence of age distribution in the onedimensional supercritical age dependent branching process, Annals of Probability, No. 1, 38-50.  Home/Search   Document Not in Database   Summary   Related Articles

....X i=1 V (x i ) 4.5) where Y t j fx 1 ; x 2 ; x Z(t) g is the age distribution at time t, is a nonnegative martingale. Also the empirical age distribution A(x; t) j #fi : Y i xg Z(t) 4.6) converges in distribution as t 1 w.p.1. to the stable age distribution (Athreya and Kaplan [19]) A(x) j R x 0 e Gammaffu (1 Gamma G(u) du R 1 0 e Gammaffu (1 Gamma G(u) du : 4.7) Theorem 16. Let m 1 and W ( Delta) be as in (4.5) Then fW (t) t 0g is a nonnegative martingale and converges w.p.1. to a limit W and P (W = 0jZ 0 = 1) is one or q according as Sigmaj (log j)p ....

Athreya,K.B. and Kaplan,N.(1976): Convergence of age distribution in the onedimensional supercritical age dependent branching process, Annals of Probability, No. 1, 38-50.

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