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On the Increments of the Principal Value of Brownian Local Time

  
@article{EJP269,
	author = {Endre Csaki and Yueyun Hu},
	title = {On the Increments of the Principal Value of Brownian Local Time},
	journal = {Electron. J. Probab.},
	fjournal = {Electronic Journal of Probability},
	volume = {10},
	year = {2005},
	keywords = {},
	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 $Y$.},
	pages = {no. 27, 925-947},
	issn = {1083-6489},
	doi = {10.1214/EJP.v10-269},    
        url = {http://ejp.ejpecp.org/article/view/269}}