Research output: Contribution to Journal/Magazine › Journal article › peer-review
<mark>Journal publication date</mark> | 10/2013 |
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<mark>Journal</mark> | Proceedings of the Steklov Institute of Mathematics |
Issue number | 1 |
Volume | 282 |
Number of pages | 25 |
Pages (from-to) | 273-297 |
Publication Status | Published |
Early online date | 22/10/13 |
<mark>Original language</mark> | English |
As is well known, for a supercritical Galton-Watson process Z (n) whose offspring distribution has mean m > 1, the ratio W (n) := Z (n) /m (n) has almost surely a limit, say W. We study the tail behaviour of the distributions of W (n) and W in the case where Z (1) has a heavy-tailed distribution, that is, for every lambda > 0. We show how different types of distributions of Z (1) lead to different asymptotic behaviour of the tail of W (n) and W. We describe the most likely way in which large values of the process occur.