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

Marie-Pierre Etienne (1) , Pierre P. Vallois (2, 3)

1 LSG - Laboratoire Statistique et Génome
2 IECN - Institut Élie Cartan de Nancy
3 OMEGA - Probabilistic numerical methods

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

Mots clés: Skorokhod's embedding; local score; random walk; one-sided maximum

Domaines: Probabilités [math.PR]

Marie-Pierre Etienne, Pierre P. Vallois. Approximation of the distribution of the supremum of a centered random walk. Application to the local score. Methodology and Computing in Applied Probability, 2004, 6 (3), pp.255-275. ⟨10.1023/B:MCAP.0000026559.87023.ec⟩. ⟨hal-00141218⟩