Mathematics > Probability
[Submitted on 8 Jul 2014 (v1), last revised 23 Dec 2014 (this version, v2)]
Title:Last zero time or Maximum time of the winding number of Brownian motions
View PDFAbstract: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.
Submission history
From: Izumi Okada [view email][v1] Tue, 8 Jul 2014 13:52:37 UTC (7 KB)
[v2] Tue, 23 Dec 2014 23:28:01 UTC (7 KB)
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