TY - JOUR
T1 - Last Zero Time or Maximum Time of the Winding Number of Brownian Motions
AU - Okada, Izumi
N1 - Publisher Copyright:
© 2014, University of Washington. All Rights Reserved.
PY - 2014/9/18
Y1 - 2014/9/18
N2 - 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.
AB - 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.
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U2 - 10.1214/ECP.v19-3485
DO - 10.1214/ECP.v19-3485
M3 - Article
AN - SCOPUS:84938613471
VL - 19
JO - Electronic Communications in Probability
JF - Electronic Communications in Probability
SN - 1083-589X
ER -