2014/07/08 by Izumi Okada, Okada, Izumi
Economics, Econometrics and Finance · Mathematics · #FOS: Mathematics #Mathematical Dynamics and Fractals #Probability (math.PR) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics #math.PR
paper · pdf · doi:10.48550/arxiv.1407.2083
Electron. Commun. Probab. 2014
openalex publication_date 2014/07/08 · arxiv created 2014/12/23 · arxiv updated 2014/12/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.