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- W2758653759 abstract "Let $(W_n(theta))_{n in mathbb{N}_0}$ be Biggins' martingale associated with a supercritical branching random walk, and let $W(theta)$ be its almost sure limit. Under a natural condition for the offspring point process in the branching random walk, we show that if the law of $W_1(theta)$ belongs to the domain of normal attraction of an $alpha$-stable distribution for some $alpha in (1,2)$, then, as $ntoinfty$, there is weak convergence of the tail process $(W(theta) - W_{n-k}(theta))_{k in mathbb{N}_0}$, properly normalized, to a random scale multiple of a stationary autoregressive process of order one with $alpha$-stable marginals." @default.
- W2758653759 created "2017-10-06" @default.
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- W2758653759 date "2017-09-21" @default.
- W2758653759 modified "2023-09-27" @default.
- W2758653759 title "Stable-like fluctuations of Biggins' martingales" @default.
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