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Excursions above high levels by Gaussian random fields

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  • Adler, Robert J.

Abstract

For a two-dimensional, homogeneous, Gaussian random field X(t) and compact, convex S [subset of] R2 we show that as u --> [infinity] the set Au = {t [set membership, variant] S : X(t) [greater-or-equal, slanted] u} possesses, with probabilityapproaching one, components that are approximately convex. Furthermore, the function X is also approximately concave over Au. One of the main aims of the paper is, at the cost of losing some detail, to simplify the analytic complexity of previous results about high level excursions of Gaussian fields by judicious use of concepts from integral and differential geometry.

Suggested Citation

  • Adler, Robert J., 1977. "Excursions above high levels by Gaussian random fields," Stochastic Processes and their Applications, Elsevier, vol. 5(1), pages 21-25, February.
    • Handle: RePEc:eee:spapps:v:5:y:1977:i:1:p:21-25
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    Cited by:

    1. Grigory Franguridi, 2014. "Higher order conditional moment dynamics and forecasting value-at-risk (in Russian)," Quantile, Quantile, issue 12, pages 69-82, February.
    2. Ilze Kalnina & Natalia Sizova, 2015. "Estimation of volatility measures using high frequency data (in Russian)," Quantile, Quantile, issue 13, pages 3-14, May.

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