High minima of non-smooth Gaussian processes
Wu, Zhixin; Chakrabarty, Arijit; Samorodnitsky, Gennady
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.
Chakrabarty's research was partially supported by the MATRICS grant of the the Science and Engineering Research Board, Government of India. Samorodnitsky's research was partially supported by the ARO grant W911NF-18 -10318 at Cornell University
Gaussian process; high excursion; minima