High minima of non-smooth Gaussian processes
Probability
2019-08-27 v2
Abstract
In this short note we study the asymptotic behaviour of the minima over compact intervals of Gaussian processes, whose paths are not necessarily smooth. We show that, beyond the logarithmic large deviation Gaussian estimates, this problem is closely related to the classical small-ball problem. Under certain conditions we estimate the term describing the correction to the large deviation behaviour. In addition, the asymptotic distribution of the location of the minimum, conditionally on the minimum exceeding a high threshold, is also studied.
Cite
@article{arxiv.1902.10894,
title = {High minima of non-smooth Gaussian processes},
author = {Zhixin Wu and Arijit Chakrabarty and Gennady Samorodnitsky},
journal= {arXiv preprint arXiv:1902.10894},
year = {2019}
}
Comments
A few typos are corrected. The paper will appear in Electronic Communications in Probability