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arxiv: math/0501199 · v1 · submitted 2005-01-13 · 🧮 math.PR

On the increments of the principal value of Brownian local time

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keywords brownianepsilonincrementslocalprincipaltimevaluecauchy
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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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