Asymptotic results for the last zero crossing time of a Brownian motion with non-null drift

摘要

We consider the last zero crossing time T-mu,T-t of a Brownian motion, with drift mu not equal 0, in the time interval [0, t]. We prove the large deviation principle of {T mu(root)r,t : r > 0} as r tends to infinity. Moreover, motivated by the results on moderate deviations in the literature, we also prove a class of large deviation principles for the same random variables with different scalings, which are governed by the same rate function. Finally we compare some aspects of the classical moderate deviation results, and the results in this paper. (C) 2020 Elsevier B.V. All rights reserved.