Electronic Journal of Probability

On the Increments of the Principal Value of Brownian Local Time

Endre Csaki and Yueyun Hu

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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 $Y$.

Article information

Source
Electron. J. Probab., Volume 10 (2005), paper no. 27, 925-947.

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

Permanent link to this document
https://projecteuclid.org/euclid.ejp/1464816828

Digital Object Identifier
doi:10.1214/EJP.v10-269

Mathematical Reviews number (MathSciNet)
MR2164034

Zentralblatt MATH identifier
1109.60066

Rights
This work is licensed under aCreative Commons Attribution 3.0 License.

Citation

Csaki, Endre; Hu, Yueyun. On the Increments of the Principal Value of Brownian Local Time. Electron. J. Probab. 10 (2005), paper no. 27, 925--947. doi:10.1214/EJP.v10-269. https://projecteuclid.org/euclid.ejp/1464816828


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