Tail asymptotics for the supercritical Galton – Watson process in the heavy - tailed case 1
نویسندگان
چکیده
As well known, for a supercritical Galton–Watson process Zn whose offspring distribution has mean m > 1, the ratio Wn := Zn/m n has a.s. limit, say W . We study tail behaviour of the distributions of Wn and W in the case where Z1 has heavy-tailed distribution, that is, EeλZ1 = ∞ for every λ > 0. We show how different types of distributions of Z1 lead to different asymptotic behaviour of the tail of Wn and W . We describe the most likely way how large values of the process occur.
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