Theoretical Statistics and Mathematics Unit, ISI Delhi

Asymptotic behaviour of Gaussian minima

by Arijit Chakrabarty and Gennady Samorodnitsky

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.

isid/ms/2016/04 [fulltext]

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