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Last zero time or maximum time of the winding number of Brownian motions

   
@article{ECP3485,
	author = {Izumi Okada},
	title = {Last zero time or maximum time of the winding number of Brownian motions},
	journal = {Electron. Commun. Probab.},
	fjournal = {Electronic Communications in Probability},
	volume = {19},
	year = {2014},
	keywords = {},
	abstract = {In this paper we consider  the winding number, $\theta(s)$, of planar Brownian motion and  study asymptotic behavior  of the process of  the maximum time, the time when $\theta(s)$ attains  the maximum  in the interval  $0\le s \le t$.  We find the limit law of its logarithm with a suitable normalization factor  and   the upper growth rate of  the maximum time process  itself.  We also show that the process of  the last zero time of  $\theta(s)$ in $[0,t]$ has the same law as the maximum time process.},
	pages = {no. 64, 1-8},
	issn = {1083-589X},
	doi = {10.1214/ECP.v19-3485},    
        url = {http://ecp.ejpecp.org/article/view/3485}}