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

Izumi Okada

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arXiv · 1407.2083

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

Izumi Okada

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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.

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Izumi Okada. 2014-07-08. Last zero time or Maximum time of the winding number of Brownian motions. https://arxiv.org/abs/1407.2083

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