Last Zero Time or Maximum Time of the Winding Number of Brownian Motions

Izumi Okada

doi:10.1214/ECP.v19-3485

Last Zero Time or Maximum Time of the Winding Number of Brownian Motions

Research output: Contribution to journal › Article

Abstract

In this paper we consider the winding number, θ(s), of planar Brownian motion and study asymptotic behavior of the process of the maximum time, the time when θ(s) attains the maximum in the interval 0 ≤ s ≤ 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 θ(s) in [0; t] has the same law as the maximum time process.

Original language	English
Journal	Electronic Communications in Probability
Volume	19
DOIs	https://doi.org/10.1214/ECP.v19-3485
Publication status	Published - Sep 18 2014
Externally published	Yes

All Science Journal Classification (ASJC) codes

Statistics and Probability
Statistics, Probability and Uncertainty

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Okada, I. (2014). Last Zero Time or Maximum Time of the Winding Number of Brownian Motions. Electronic Communications in Probability, 19. https://doi.org/10.1214/ECP.v19-3485

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