Asymptotic behaviour of Gaussian minima
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Abstract
We investigate what happens when an entire sample path of a smooth
Gaussian process on a compact interval lies above a high
level. Specifically, we determine the precise asymptotic probability
of such an event, the extent to which the high level is exceeded,
the conditional shape of the process above the high level, and the
location of the minimum of the process given that the sample path is
above a high level.
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Chakrabarty's research was partially supported by the INSPIRE grant of the Department of Science and Technology, Government of India.
Samorodnitsky's research was partially supported by the ARO
grant W911NF-12-10385 and by the NSF grant DMS-1506783
at Cornell University.
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2016
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Keywords
Gaussian process; high excursion; minima; precsie asymptotics
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