Asymptotic behaviour of Gaussian minima
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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.
Gaussian process; high excursion; minima; precsie asymptotics
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