#
Back to the local score in the logarithmic case : a direct and
simple proof

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Jean-Noel BACRO, Jean-Jacques DAUDIN, Sabine MERCIER, Stéphane ROBIN

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*Ann. Inst. Statist. Math*, 2002.

**Abstract**

Let
*X*_{1}, ... *X*_{n} be a sequence of
i.i.d. positive or negative integer valued random variables and
*H*_{n} = max_{0 <= i <= j
<= n}(*X*_{i} + ... +
*X*_{j}) the local score of the sequence. A recent
result shows that *H*_{n} is actually the maximum
of an integer valued Lindley process. Therefore known results about
the asymptotic distribution of the maximum of a weakly dependent
process give readily the expected result about the asymptotic behavior
of the local score, with a simple way for computing the needed
constants.

**Key words and phrases**
Extremal index, Lindley process, local score, Markov
chain