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Infinite divisibility of infinite sums of lower records: a simple proof
Published online by Cambridge University Press: 14 July 2016
Abstract
Let {X
n
, n = 0, 1,…} be the sequence of the lower records for an arbitrary underlying distribution μ on [0, ∞). We show that is equal in distribution to
where {τ
i
, i = 1, 2,…} is a Poisson flow of unit intensity and g is a right-continuous and nonincreasing function defined by μ. This observation allows us to extend results of Bose et al. and simplify their proofs.
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- Copyright © Applied Probability Trust 2004
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