Let (Xn)n ≥ 0 be a real random walk starting at 0, with centered increments bounded by a constant K. The main result of this study is: |P(Sn √ n ≥ x)−P(σ sup0 ≤ u ≤ 1Bu ≥ x)|≤ C(n,K)√ ∈ n/n, where x ≥ 0, σ2 is the variance of the increments, Sn is the supremum at time n of the random walk, (Bu,u≥ 0) is a standard linear Brownian motion and C(n,K) i...

Mercier, SabineCellier, DominiqueCharlot, François

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., ...

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...