Article Type

Research Article

Publication Title

Electronic Communications in Probability

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.

DOI

10.1214/19-ECP251

Publication Date

1-1-2019

Comments

Open Access, Bronze, Green

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