Probability that the maximum of the reflected Brownian motion over a finite interval $[0,t]$ is achieved by its last zero before $t$

Agnès Lagnoux, Sabine Mercier, Pierre Vallois

We calculate the probability $p_c$ that the maximum of a reflected Brownian motion $U$ is achieved on a complete excursion, i.e. $p_c:=P(\overline{U}(t)=U^{\ast }(t))$ where $\ov…