High minima of non-smooth Gaussian processes
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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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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
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2019-02-27
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Keywords
Gaussian process; high excursion; minima
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preprint