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On the increments of the principal value of Brownian local time

Endre Csáki·Yueyun Hu
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Abstract

Let $W$ 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 $Y$.

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Endre Csáki, Yueyun Hu. 2005-01-13. On the increments of the principal value of Brownian local time. https://arxiv.org/abs/math/0501199

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