## Approximation of the distribution of the supremum of a centered random walk. Application to the local score.

We determine the rate of convergence of the distribution function of the one-sided supremum of a centered random walk to its limit.

We determine the rate of convergence of the distribution function of the one-sided supremum of a centered random walk to its limit.

Using random walk theory, we first establish explicitly the exact distribution of the maximal partial sum of a sequence of independent and identically distributed random variables. This result allows us to obtain a new approximation of the distribution of the local score of one sequence. This approximation improves the one given par Karlin et al., ...

Asymptotic behavior of the local score via Brownian motion

Published in Annals of the Institute of Statistical Mathematics

Let X1, ... , Xn be a sequence of i.i.d. integer valued random variables and Hn the local score of the sequence. A recent result shows that Hn 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 th...

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