Abstract
AbstractGiven a branching random walk
$(Z_n)_{n\geq0}$
on
$\mathbb{R}$
, let
$Z_n(A)$
be the number of particles located in interval A at generation n. It is well known that under some mild conditions,
$Z_n(\sqrt nA)/Z_n(\mathbb{R})$
converges almost surely to
$\nu(A)$
as
$n\rightarrow\infty$
, where
$\nu$
is the standard Gaussian measure. We investigate its large-deviation probabilities under the condition that the step size or offspring law has a heavy tail, i.e. a decay rate of
$\mathbb{P}(Z_n(\sqrt nA)/Z_n(\mathbb{R})>p)$
as
$n\rightarrow\infty$
, where
$p\in(\nu(A),1)$
. Our results complete those in Chen and He (2019) and Louidor and Perkins (2015).
Publisher
Cambridge University Press (CUP)
Subject
Statistics, Probability and Uncertainty,General Mathematics,Statistics and Probability
Cited by
2 articles.
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