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2014 Last zero time or maximum time of the winding number of Brownian motions
Izumi Okada
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Electron. Commun. Probab. 19: 1-8 (2014). DOI: 10.1214/ECP.v19-3485

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. "Last zero time or maximum time of the winding number of Brownian motions." Electron. Commun. Probab. 19 1 - 8, 2014. https://doi.org/10.1214/ECP.v19-3485

Information

Accepted: 18 September 2014; Published: 2014
First available in Project Euclid: 7 June 2016

zbMATH: 1323.60112
MathSciNet: MR3262070
Digital Object Identifier: 10.1214/ECP.v19-3485

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