# Un processus ponctuel associé aux maxima locaux du mouvement brownien - Mathematics > Probability

Abstract: Let $B = B t {t \in {\bf R}}$ be a symmetric Brownian motion, i.e.$B t {t \in {\bf R} +}$ and $B {-t} {t \in {\bf R} +}$ are independentBrownian motions starting at $0$. Given $a \ge b>0$, we describe the law of therandom set $${\cal M} {a,b} = \{t \in {\bf R} : B t = \max {s \in t-a,t+b}B s\},$$ and we describe the L\-evy measure of a subordinator whose closedrange is the regenerative set $${\cal R} a = \{t \in {\bf R}\ + : B t = \max {s\in t-a +,t} B s\}.$$

Author: Christophe Leuridan

Source: https://arxiv.org/