2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/73841Let $W$ be a one-dimensional Brownian motion starting from 0. Define $Y(t)= \int_0^t{\d s \over W(s)} := \lim_{ε\to0} \int_0^t 1_{(|W(s)|> ε)} {\d s \over W(s)} $ as Cauchy's principal value related to local time. We prove limsup and liminf results for the increments of $Y$.23 pagesProbability60J65; 60J55; 60F15text