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Asymptotic behaviour of high Gaussian minima

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  • Chakrabarty, Arijit
  • Samorodnitsky, Gennady

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.

Suggested Citation

  • Chakrabarty, Arijit & Samorodnitsky, Gennady, 2018. "Asymptotic behaviour of high Gaussian minima," Stochastic Processes and their Applications, Elsevier, vol. 128(7), pages 2297-2324.
    • Handle: RePEc:eee:spapps:v:128:y:2018:i:7:p:2297-2324
    DOI: 10.1016/j.spa.2017.09.008
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    References listed on IDEAS

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    1. Archil Gulisashvili & Peter Tankov, 2013. "Tail behavior of sums and differences of log-normal random variables," Papers 1309.3057, arXiv.org, revised Jan 2016.
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    Cited by:

    1. Selk, Zachary, 2024. "Large deviations for high minima of Gaussian processes with nonnegatively correlated increments," Statistics & Probability Letters, Elsevier, vol. 206(C).

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