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2005 On the Increments of the Principal Value of Brownian Local Time
Endre Csaki, Yueyun Hu
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Electron. J. Probab. 10: 925-947 (2005). DOI: 10.1214/EJP.v10-269

Abstract

Let $W$ be a one-dimensional Brownian motion starting from 0. Define $Y(t)= \int_0^t{ds \over W(s)}:= \lim_{\epsilon\to 0} \int_0^t 1_{(|W(s)|> \epsilon)} {ds\over W(s)}$ 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 Csaki. Yueyun Hu. "On the Increments of the Principal Value of Brownian Local Time." Electron. J. Probab. 10 925 - 947, 2005. https://doi.org/10.1214/EJP.v10-269

Information

Accepted: 14 July 2005; Published: 2005
First available in Project Euclid: 1 June 2016

zbMATH: 1109.60066
MathSciNet: MR2164034
Digital Object Identifier: 10.1214/EJP.v10-269

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