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arXiv · 1902.10894

High minima of non-smooth Gaussian processes

Zhixin Wu·Arijit Chakrabarty·Gennady Samorodnitsky
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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.

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Zhixin Wu, Arijit Chakrabarty, Gennady Samorodnitsky. 2019-02-28. High minima of non-smooth Gaussian processes. https://arxiv.org/abs/1902.10894

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