On the increments of the principal value of Brownian local time

Details On the increments of the principal value of Brownian local time On the increments of the principal value of Brownian local time

2005-01-13

arxiv.org/abs/math/0501199v1

Mathematics

Probability

23 pages

Scientific paper

Let $W$ be a one-dimensional Brownian motion starting from 0. Define $Y(t)=
\int_0^t{\d s \over W(s)} := \lim_{\epsilon\to0} \int_0^t 1_{(|W(s)|>
\epsilon)} {\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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